{"id":27282,"date":"2023-04-04T06:21:43","date_gmt":"2023-04-04T06:21:43","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=27282"},"modified":"2023-11-15T15:32:28","modified_gmt":"2023-11-15T15:32:28","slug":"two-point-form-definition-derivation-formula-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/two-point-form","title":{"rendered":"Two Point Form \u2013 Definition, Derivation, Formula, Examples"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-f7852cbf-904b-4f65-8079-a037466407d0\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/two-point-form#0-what-is-two-point-form-in-math>What Is Two Point Form in Math?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/two-point-form#3-derivation-of-two-point-form-formula>Derivation of Two Point Form Formula<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/two-point-form#6-finding-equation-of-a-line-using-two-point-form>Finding Equation of a Line Using Two Point Form<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/two-point-form#10-solved-examples-on-two-point-form>Solved Examples On Two Point Form<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/two-point-form#11-practice-problems-on-two-point-form>Practice Problems On Two Point Form<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/two-point-form#12-frequently-asked-questions-on-two-point-form>Frequently Asked Questions On Two Point Form<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-two-point-form-in-math\">What Is Two Point Form in Math?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Two point form in math is one of the important methods to find the equation of a line when coordinates of any two points on the line are known.<\/strong> The equation of a line is used to represent each and every point on the line, we can say that it is satisfied by each point on the line.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let $A(x_1,\\; y_1)$ and $B (x_2,\\; y_2)$ be any two distinct points on the line l.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"523\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/understanding-the-two-point-form.png\" alt=\"Understanding the two point form\" class=\"wp-image-35720\" title=\"Understanding the two point form\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/understanding-the-two-point-form.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/understanding-the-two-point-form-300x253.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">The two-point form is given by<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{y\\;-\\;y_1}{x\\;-\\;x_1} = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1}$<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"1-two-point-form-definition\">Two Point Form: Definition<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">If $(x_1,\\; y_1)$ and $(x_2,\\; y_2)$ be the coordinates of any two distinct points on the line, then the equation of line in two-point form is<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{y\\;-\\;y1}{x\\;-\\;x_1} = \\frac{y2\\;-\\;y_1}{x_2\\;-\\;x_1}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">OR<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(y\\;-\\;y_2) = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1} (x\\;-\\;x_2)$<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-multiples-of-100-in-unit-form\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_multiples_100_pt.png\" alt=\"Add Multiples of 100 in Unit Form Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Multiples of 100 in Unit Form Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-two-numbers-up-to-5\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_complete_add_w5_pt.png\" alt=\"Add Two Numbers (Up to 5) Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Two Numbers (Up to 5) Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-two-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_add_numbers_1_pt.png\" alt=\"Add Two Numbers Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Two Numbers Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/change-decimals-from-word-form-to-fraction-form\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/decimals_convert_words_to_frac_tenths_pt.png\" alt=\"Change Decimals from Word Form to Fraction Form Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Change Decimals from Word Form to Fraction Form Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/change-expanded-to-standard-form\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/place_value_expand_to_std_5d_pt.png\" alt=\"Change Expanded to Standard Form Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Change Expanded to Standard Form Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/change-to-standard-form\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/place_value_write_in_word_5d_pt.png\" alt=\"Change to Standard Form Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Change to Standard Form Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/choose-the-correct-standard-form-of-the-decomposed-hundredths\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/decimals_compose_hundredths_pt.png\" alt=\"Choose the Correct Standard Form of the Decomposed Hundredths Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Choose the Correct Standard Form of the Decomposed Hundredths Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/choose-the-standard-form-of-the-decomposed-decimal-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/decimals_convert_to_standard_form_pt.png\" alt=\"Choose the Standard Form of the Decomposed Decimal Numbers Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Choose the Standard Form of the Decomposed Decimal Numbers Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-expanded-decimal-form\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/decimals_complete_expanded_dec_form_pt.png\" alt=\"Complete the Expanded Decimal Form Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Complete the Expanded Decimal Form Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-expanded-form\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/place_value_complete_expanded_form_pt.png\" alt=\"Complete the Expanded Form Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Complete the Expanded Form Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-two-point-form-formula\">Two Point Form Formula<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The two points formula of two point form of an equation is given as-<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let $(x_1,\\; y_1)$ and $(x_1,\\; y_1)$ be the two points such that the equation of line passing through these two points is given by the formula mentioned below-<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(y\\;-\\;y_1) = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1} (x\\;-\\;x_1)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, $(x,\\; y)$ is just an arbitrary point on the line.&nbsp;<\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-with-regrouping-horizontal-addition-and-subtraction\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-with-regrouping-horizontal-addition-and-subtraction.jpeg\" alt=\"Add and Subtract Two 2-Digit Numbers with Regrouping: Horizontal Addition and Subtraction Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-with-regrouping-missing-digits\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-with-regrouping-missing-digits.jpeg\" alt=\"Add and Subtract Two 2-Digit Numbers with Regrouping: Missing Digits Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-with-regrouping-missing-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-with-regrouping-missing-numbers.jpeg\" alt=\"Add and Subtract Two 2-Digit Numbers with Regrouping: Missing Numbers Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-with-regrouping-vertical-addition-and-subtraction\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-with-regrouping-vertical-addition-and-subtraction.jpeg\" alt=\"Add and Subtract Two 2-Digit Numbers with Regrouping: Vertical Addition and Subtraction Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-without-regrouping-horizontal-addition-and-subtraction\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-without-regrouping-horizontal-addition-and-subtraction.jpeg\" alt=\"Add and Subtract Two 2-Digit Numbers without Regrouping: Horizontal Addition and Subtraction Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-without-regrouping-horizontal-timed-practice\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-without-regrouping-horizontal-timed-practice.jpeg\" alt=\"Add and Subtract Two 2-Digit Numbers without Regrouping: Horizontal Timed Practice\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-without-regrouping-missing-digits\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-without-regrouping-missing-digits.jpeg\" alt=\"Add and Subtract Two 2-Digit Numbers without Regrouping: Missing Digits Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-without-regrouping-missing-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-without-regrouping-missing-numbers.jpeg\" alt=\"Add and Subtract Two 2-Digit Numbers without Regrouping: Missing Numbers Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-without-regrouping-vertical-addition-and-subtraction\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-without-regrouping-vertical-addition-and-subtraction.jpeg\" alt=\"Add and Subtract Two 2-Digit Numbers without Regrouping: Vertical Addition and Subtraction Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-without-regrouping-vertical-timed-practice\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-and-subtract-two-2-digit-numbers-without-regrouping-vertical-timed-practice.jpeg\" alt=\"Add and Subtract Two 2-Digit Numbers without Regrouping: Vertical Timed Practice\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-derivation-of-two-point-form-formula\">Derivation of Two Point Form Formula<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Let $M (x_1,\\; y_1)$ and $N (x_2,\\; y_2)$ be the two given points on the line L.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let $P (x,\\; y)$ be a random point on the line L.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"563\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/derivation-of-two-point-form.png\" alt=\"Derivation of two point form\" class=\"wp-image-35722\" title=\"Derivation of two point form\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/derivation-of-two-point-form.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/derivation-of-two-point-form-300x272.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">From the figure, we can observe that the three points $P_1,\\; P_2$ and P lie on the same line. They are collinear.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Slope of line MP $=$ Slope of line NP<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{y\\;-\\;y1}{x\\;-\\;x1} = \\frac{y2\\;-\\;y1}{x2\\;-\\;x1}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Or<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(y\\;-\\;y_1) = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1} (x\\;-\\;x_1)$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-equation-of-a-line-in-two-point-form\">Equation of a Line in Two-Point Form<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The equation of a line in the two-point form is given by<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(y\\;-\\;y1) = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1} (x\\;-\\;x_1)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">or<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(y\\;-\\;y_2) = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1} (x\\;-\\;x_2)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">where<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(x,\\; y)$: coordinates of any point on a line<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(x_1,\\; y_1)$ and $(x_2,\\; y_2)$: coordinates of two points on the line<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-how-to-write-equation-of-a-line-in-two-point-form\">How To Write Equation of a Line in Two Point Form<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s understand the steps to find the equation of a line using two-point form.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Name the coordinates of the given two points as $(x_1,\\; y_1)$ and $(x_2,\\; y_2)$.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Substitute the values in the Two-Point formula given by&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">$(y \\;-\\; y_1) = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1} (x\\;-\\;x_1)$<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Simplify.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-finding-equation-of-a-line-using-two-point-form\">Finding Equation of a Line Using Two Point Form<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">To write equation of a line in two-point form, simply substitute the coordinates of the given two points in the equation $(y\\;-\\;y_2) = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1} (x\\;-\\;x_2)$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example: Find the equation of a line passing through the points <\/strong>$(1,\\; 2)$<strong> and <\/strong>$(3,\\; 4)$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, $(x_1,\\; y_1) =&nbsp; (1,\\; 2)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(x_2,\\; y_2) = (3,\\; 4)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Substitute the values in $(y\\;-\\;y_2) = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1} (x\\;-\\;x_2)$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;$(y\\;-\\;4) = \\frac{4\\;-\\;2}{3\\;-\\;1} (x\\;-\\;3)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;$(y\\;-\\;4) = (x\\;-\\;3)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"> $y = x + 1$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-deriving-two-point-form-using-point-slope-form\">Deriving Two Point Form Using Point Slope Form<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Let $A (x_1,\\; y_1)$ and $B (x_2,\\; y_2)$ be two given distinct points on a line as given below:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"419\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/two-point-form-equation.png\" alt=\"Two-point form equation\" class=\"wp-image-35723\" title=\"Two-point form equation\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/two-point-form-equation.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/two-point-form-equation-300x203.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">The two-point slope form of the straight line passing through these points is given by \u201cm\u201d:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$m = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1}$ __________(1)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The Point-Slope form equation of a line is given by:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(y\\;-\\;y_1) = m (x\\;-\\;x_1)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Substituting 1 in 2:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(y\\;-\\;y_1) = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1} (x\\;-\\;x_1)$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-facts-about-two-point-form\">Facts about Two Point Form!<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The two-point form of a line can also be written as given:<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{y\\;-\\;y_1}{x\\;-\\;x_1} = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Or<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{y\\;-\\;y_2}{x\\;-\\;x_2} = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1}$<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">An exceptional case where the two-point form cannot be used is the equation of a vertical line passing through point (a, b) given by $x = a$. Slope of the vertical line is not defined.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In this article, we learned about two-point forms of a line. Let us now look at some examples and practice some problems to understand the concept better.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-solved-examples-on-two-point-form\">Solved Examples On Two Point Form<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>1. Find the equation of the line passing through the points:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(\\;-\\;2,\\; 3)$<strong> and <\/strong>$(3,\\; 5)$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The given points are:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(x_1,\\; y_1) = (2,\\; 3)$ and $(x_2,\\; y_2) = (3,\\; 5)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The equation of a straight line passing through the points $(x_1,\\; y_1)$ and $(x_2,\\; y_2)$ can be written using two-point form as:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(y\\;-\\;y_2)= \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1}(x\\;-\\;x_2)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Substituting the values, we get:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(y\\;-\\;3) = \\frac{5\\;-\\;3}{3\\;-\\;(\\;-\\;2)}(x\\;-\\;2)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(y\\;-\\;3)= \\frac{2}{5} (x\\;-\\;2)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$5 (y\\;-\\;3) = 2 (x\\;-\\;2)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$5y \\;\u2013\\; 15 = 2x + 4$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$2x + 4 \\;\u2013\\; 5y + 15 = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$2x \\;\u2013\\; 5y + 19 = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, this is the required equation of a line passing through the given points.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2. What is the equation of a straight line passing through the points <\/strong><strong>(3, 0)<\/strong><strong> and <\/strong><strong>(0, 3)<\/strong><strong>?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s write the coordinates as<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(x_1,\\; y_1) = (3,\\; 0)$ and $(x_2,\\; y_2) = (0, 3)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The equation of a straight line passing through the points $(x_1,\\; y_1)$ and $(x_2,\\; y_2)$ can be written as:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(y\\;-\\;y2) = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1} (x\\;-\\;x_2)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Substituting the values, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(y\\;-\\;0) = \\frac{3\\;-\\;0}{0\\;-\\;3} (x\\;-\\;3)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$y = \\frac{3\\;-\\;}{3} (x\\;-\\;3)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$y =\\;-\\;1(x \\;\u2013\\; 3)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$y =\\;-\\;x + 3$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x + y \\;\u2013\\; 3 = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, the equation of a line passing through the given points $(3,\\; 0)$<strong> and <\/strong>$(0,\\; 3)$ is $x + y \\;\u2013\\; 3 = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3. Find the equation of a line with two points <\/strong>$(3,\\; 5)$<strong> and <\/strong>$(2,\\; 3)$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Given : Two points on the straight line are $(3,\\; 5)$ and $(2,\\; 3)$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The equation of a straight line passing through the points $(x_1,\\; y_1)$ and $(x_2\\;, y_2)$ can be written as:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(y \\;-\\; y_1) = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1} (x\\;-\\;x_1)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Substitute $(x_1,\\; y_1) = (3,\\; 5)$ and $(x_2,\\; y_2) = (2,\\; 3)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(y\\;-\\;5) = \\frac{3\\;-\\;5}{2\\;-\\;3} (x\\;-\\;3)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(y\\;-\\;5) =\\frac{\\;-2}{\\;-1} (x\\;-\\;3)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$y\\;-\\;5 = 2(x\\;-\\;3)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$y\\;-\\;5&nbsp; = 2x\\;-\\;6$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$2x\\;-\\;y = 6\\;-\\;5$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$2x\\;-\\;y = 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$2x \\;-\\; y&nbsp;\\;-\\;1 = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>4. Find the equation of a straight line whose x-intercept is \u201ca\u201d and y-intercept is \u201cb.\u201d<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong> The line passes through the points $(a,\\; 0)$ and $(0,\\; b)$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Substituting the values $(x_1,\\; y_1) = (a,\\; 0)$ and $(x_2,\\; y_2) = (0,\\; b)$ in the two point form we get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(y\\;-\\;y_1) = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1} (x\\;-\\;x_1)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(y\\;-\\;0) = \\frac{b\\;-\\;0}{0\\;-\\;a} (x\\;-\\;a)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$y&nbsp; = \\frac{b}{-a} (x\\;-\\;a)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$-ay = b(x \\;-\\; a)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$-ay = bx \\;-\\; ba$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$bx + ay = ab$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Dividing both sides by ab, we get:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{bx + ay}{ab} = \\frac{ab}{ab}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{x}{a} + \\frac{y}{a} = 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, the equation of the given line is given as:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\therefore \\frac{x}{a} + \\frac{y}{a} = 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">This is also known as the intercept-form of a line.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>5. Derive the y-intercept of the line with the coordinates given by: <\/strong>$A\\; (3, \\;-\\;2)$<strong> and B <\/strong>$(\\;-\\;1,\\; 3)$<strong> passing through it and also find the slope m of the line.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let the given points be:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(x_1,\\; y_1) = ( 3,\\;-\\;2)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(x_2,\\; y_2) = (\\;-\\;1, 3)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The equation of a straight line passing through the points $(x_1,\\; y_1)$ and $(x_2,\\; y_2)$ can be written as:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(y \\;-\\; y_1) = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1} (x\\;-\\;x_1)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(y\\;-\\;(\\;-\\;2)) = \\frac{3\\;-\\;(\\;-\\;2)}{\\;-\\;1\\;-\\;3} (x\\;-\\;(\\;-\\;1))$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(y + 2) = \\frac{5}{-\\;4} (x + 1)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, multiplying both sides by $-4$ gives us,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\;-4 (y + 2) = 5 (x + 1)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\;-4y \\;\u2013\\; 8 = 5x + 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\;-4y = 5x +13$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$5x +4y +13 =0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$y = \\frac{-5}{4}x + \\frac{13}{4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The line equation from two points is given above.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The final equation of the slope-intercept form is written as-<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$y = mx + b$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Comparing our equation to the standard form, we will get y-intercept, b as $\\frac{7}{4}$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Further, the slope of the line (m) can be given as $\\frac{-5}{4}$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-practice-problems-on-two-point-form\">Practice Problems On Two Point Form<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Two Point Form \u2013 Definition, Derivation, Formula, Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">What is the equation of the line in the slope point form?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$ax + by + c = 0$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$y = mx + c$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$(y\\;-\\;y_1) = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1} (x\\;-\\;x_1)$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$(y\\;-\\; y_1) = (x\\;-\\;x_1)$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $(y\\;-\\;y_1) = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1} (x\\;-\\;x_1)$<br\/>The equation of a straight line passing through the points $(x_1,\\; y_1)$ and $(x_2,\\; y_2)$ can be written using two-point form as\r\n$(y\\;-\\;y_1) = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1}(x\\;-\\;x_1)$ <\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What is the equation of a straight line passing through the points (5, 0) and (0, 5)?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$x\\;-\\;y\\;\u2013\\;5 = 0$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$x + y\\;\u2013\\;5 = 0$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$x + y + 5 = 0$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\;-\\;x + y \u2013 5 = 0$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $x + y\\;\u2013\\;5 = 0$<br\/>Substitute $(x_1,\\; y_1) = (5,\\; 0)$ and $(x_2,\\; y_2) = (0,\\; 5)$ in the two point form.<br>\r\n$(y\\;-\\;y_2) = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1} (x\\;-\\;x_2)$<br>\r\nSubstituting the values, we get;<br>\r\n$(y\\;-\\;0) = \\frac{5\\;-\\;0}{0\\;-\\;5} (x\\;-\\;5)$<br>\r\n$y = \\frac{5}{-5} (x\\;-\\;5)$ <br>\r\n$y = (\\;-\\;1)(x \\;\u2013\\; 5)$<br>\r\n$y = \\;-x + 5$<br>\r\n$x + y \\;\u2013 5 = 0$<br>\r\nTherefore, the equation of a line passing through the given points $(5,\\; 0)$ and $(0,\\; 5)$ is $x + y \\;\u2013\\; 5 = 0$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">What is the slope of a line passing through the points $(\\;-5,\\; 4)$ and $(3,\\; -2)$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{-3}{4}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{3}{4}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{-4}{3}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{4}{3}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\frac{-3}{4}$<br\/>The slope of a straight line passing through the points $(x_1,\\; y_1)$ and $(x_2,\\; y_2)$ can be written as:<br>\r\nSlope $= \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1}$<br>\r\nSubstitute $(x_1,\\; y_1) = (\\;-\\;5,\\; 4)$ and $(x_2,\\; y_2) = (3,\\; \\;-\\;2)$<br>\r\nSlope $= \\frac{-2\\;-\\;4}{3 + 5}  = \\frac{-3}{4}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">What is the equation of a vertical line passing through the point $A (\\;-3,\\; \\;-5)$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$y = \\;-5$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$x = 3$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$x = \\;-3$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\;-3x\\;-\\;5y = 0$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $x = \\;-3$<br\/>The equation of a vertical line passing through the point $(a,\\; b)$ is $x = a$.<br>\r\nThe equation of a vertical line passing through the point $A\\; (\\;-3,\\; -5)$ is  $x = \\;-3$.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Two Point Form \u2013 Definition, Derivation, Formula, Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Two Point Form\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the equation of the line in the slope point form?\",\n                    \"text\": \"What is the equation of the line in the slope point form?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The equation of a straight line passing through the points $$(x_1,\\\\; y_1)$$ and $$(x_2,\\\\; y_2)$$ can be written using two-point form as\r\n$$(y\\\\;-\\\\;y_1) = \\\\frac{y_2\\\\;-\\\\;y_1}{x_2\\\\;-\\\\;x_1}(x\\\\;-\\\\;x_1)$$ \"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$ax + by + c = 0$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The equation of a straight line passing through the points $$(x_1,\\\\; y_1)$$ and $$(x_2,\\\\; y_2)$$ can be written using two-point form as\r\n$$(y\\\\;-\\\\;y_1) = \\\\frac{y_2\\\\;-\\\\;y_1}{x_2\\\\;-\\\\;x_1}(x\\\\;-\\\\;x_1)$$ \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$y = mx + c$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The equation of a straight line passing through the points $$(x_1,\\\\; y_1)$$ and $$(x_2,\\\\; y_2)$$ can be written using two-point form as\r\n$$(y\\\\;-\\\\;y_1) = \\\\frac{y_2\\\\;-\\\\;y_1}{x_2\\\\;-\\\\;x_1}(x\\\\;-\\\\;x_1)$$ \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(y\\\\;-\\\\; y_1) = (x\\\\;-\\\\;x_1)$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The equation of a straight line passing through the points $$(x_1,\\\\; y_1)$$ and $$(x_2,\\\\; y_2)$$ can be written using two-point form as\r\n$$(y\\\\;-\\\\;y_1) = \\\\frac{y_2\\\\;-\\\\;y_1}{x_2\\\\;-\\\\;x_1}(x\\\\;-\\\\;x_1)$$ \"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$(y\\\\;-\\\\;y_1) = \\\\frac{y_2\\\\;-\\\\;y_1}{x_2\\\\;-\\\\;x_1} (x\\\\;-\\\\;x_1)$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The equation of a straight line passing through the points $$(x_1,\\\\; y_1)$$ and $$(x_2,\\\\; y_2)$$ can be written using two-point form as\r\n$$(y\\\\;-\\\\;y_1) = \\\\frac{y_2\\\\;-\\\\;y_1}{x_2\\\\;-\\\\;x_1}(x\\\\;-\\\\;x_1)$$ \"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The equation of a straight line passing through the points $$(x_1,\\\\; y_1)$$ and $$(x_2,\\\\; y_2)$$ can be written using two-point form as\r\n$$(y\\\\;-\\\\;y_1) = \\\\frac{y_2\\\\;-\\\\;y_1}{x_2\\\\;-\\\\;x_1}(x\\\\;-\\\\;x_1)$$ \"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the equation of a straight line passing through the points (5, 0) and (0, 5)?\",\n                    \"text\": \"What is the equation of a straight line passing through the points (5, 0) and (0, 5)?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Substitute $$(x_1,\\\\; y_1) = (5,\\\\; 0)$$ and $$(x_2,\\\\; y_2) = (0,\\\\; 5)$$ in the two point form.<br>\r\n$$(y\\\\;-\\\\;y_2) = \\\\frac{y_2\\\\;-\\\\;y_1}{x_2\\\\;-\\\\;x_1} (x\\\\;-\\\\;x_2)$$<br>\r\nSubstituting the values, we get;<br>\r\n$$(y\\\\;-\\\\;0) = \\\\frac{5\\\\;-\\\\;0}{0\\\\;-\\\\;5} (x\\\\;-\\\\;5)$$<br>\r\n$$y = \\\\frac{5}{-5} (x\\\\;-\\\\;5)$$ <br>\r\n$$y = (\\\\;-\\\\;1)(x \\\\;\u2013\\\\; 5)$$<br>\r\n$$y = \\\\;-x + 5$$<br>\r\n$$x + y \\\\;\u2013 5 = 0$$<br>\r\nTherefore, the equation of a line passing through the given points $$(5,\\\\; 0)$$ and $$(0,\\\\; 5)$$ is $$x + y \\\\;\u2013\\\\; 5 = 0$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$x\\\\;-\\\\;y\\\\;\u2013\\\\;5 = 0$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Substitute $$(x_1,\\\\; y_1) = (5,\\\\; 0)$$ and $$(x_2,\\\\; y_2) = (0,\\\\; 5)$$ in the two point form.<br>\r\n$$(y\\\\;-\\\\;y_2) = \\\\frac{y_2\\\\;-\\\\;y_1}{x_2\\\\;-\\\\;x_1} (x\\\\;-\\\\;x_2)$$<br>\r\nSubstituting the values, we get;<br>\r\n$$(y\\\\;-\\\\;0) = \\\\frac{5\\\\;-\\\\;0}{0\\\\;-\\\\;5} (x\\\\;-\\\\;5)$$<br>\r\n$$y = \\\\frac{5}{-5} (x\\\\;-\\\\;5)$$ <br>\r\n$$y = (\\\\;-\\\\;1)(x \\\\;\u2013\\\\; 5)$$<br>\r\n$$y = \\\\;-x + 5$$<br>\r\n$$x + y \\\\;\u2013 5 = 0$$<br>\r\nTherefore, the equation of a line passing through the given points $$(5,\\\\; 0)$$ and $$(0,\\\\; 5)$$ is $$x + y \\\\;\u2013\\\\; 5 = 0$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$x + y + 5 = 0$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Substitute $$(x_1,\\\\; y_1) = (5,\\\\; 0)$$ and $$(x_2,\\\\; y_2) = (0,\\\\; 5)$$ in the two point form.<br>\r\n$$(y\\\\;-\\\\;y_2) = \\\\frac{y_2\\\\;-\\\\;y_1}{x_2\\\\;-\\\\;x_1} (x\\\\;-\\\\;x_2)$$<br>\r\nSubstituting the values, we get;<br>\r\n$$(y\\\\;-\\\\;0) = \\\\frac{5\\\\;-\\\\;0}{0\\\\;-\\\\;5} (x\\\\;-\\\\;5)$$<br>\r\n$$y = \\\\frac{5}{-5} (x\\\\;-\\\\;5)$$ <br>\r\n$$y = (\\\\;-\\\\;1)(x \\\\;\u2013\\\\; 5)$$<br>\r\n$$y = \\\\;-x + 5$$<br>\r\n$$x + y \\\\;\u2013 5 = 0$$<br>\r\nTherefore, the equation of a line passing through the given points $$(5,\\\\; 0)$$ and $$(0,\\\\; 5)$$ is $$x + y \\\\;\u2013\\\\; 5 = 0$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\;-\\\\;x + y \u2013 5 = 0$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Substitute $$(x_1,\\\\; y_1) = (5,\\\\; 0)$$ and $$(x_2,\\\\; y_2) = (0,\\\\; 5)$$ in the two point form.<br>\r\n$$(y\\\\;-\\\\;y_2) = \\\\frac{y_2\\\\;-\\\\;y_1}{x_2\\\\;-\\\\;x_1} (x\\\\;-\\\\;x_2)$$<br>\r\nSubstituting the values, we get;<br>\r\n$$(y\\\\;-\\\\;0) = \\\\frac{5\\\\;-\\\\;0}{0\\\\;-\\\\;5} (x\\\\;-\\\\;5)$$<br>\r\n$$y = \\\\frac{5}{-5} (x\\\\;-\\\\;5)$$ <br>\r\n$$y = (\\\\;-\\\\;1)(x \\\\;\u2013\\\\; 5)$$<br>\r\n$$y = \\\\;-x + 5$$<br>\r\n$$x + y \\\\;\u2013 5 = 0$$<br>\r\nTherefore, the equation of a line passing through the given points $$(5,\\\\; 0)$$ and $$(0,\\\\; 5)$$ is $$x + y \\\\;\u2013\\\\; 5 = 0$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$x + y\\\\;\u2013\\\\;5 = 0$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Substitute $$(x_1,\\\\; y_1) = (5,\\\\; 0)$$ and $$(x_2,\\\\; y_2) = (0,\\\\; 5)$$ in the two point form.<br>\r\n$$(y\\\\;-\\\\;y_2) = \\\\frac{y_2\\\\;-\\\\;y_1}{x_2\\\\;-\\\\;x_1} (x\\\\;-\\\\;x_2)$$<br>\r\nSubstituting the values, we get;<br>\r\n$$(y\\\\;-\\\\;0) = \\\\frac{5\\\\;-\\\\;0}{0\\\\;-\\\\;5} (x\\\\;-\\\\;5)$$<br>\r\n$$y = \\\\frac{5}{-5} (x\\\\;-\\\\;5)$$ <br>\r\n$$y = (\\\\;-\\\\;1)(x \\\\;\u2013\\\\; 5)$$<br>\r\n$$y = \\\\;-x + 5$$<br>\r\n$$x + y \\\\;\u2013 5 = 0$$<br>\r\nTherefore, the equation of a line passing through the given points $$(5,\\\\; 0)$$ and $$(0,\\\\; 5)$$ is $$x + y \\\\;\u2013\\\\; 5 = 0$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Substitute $$(x_1,\\\\; y_1) = (5,\\\\; 0)$$ and $$(x_2,\\\\; y_2) = (0,\\\\; 5)$$ in the two point form.<br>\r\n$$(y\\\\;-\\\\;y_2) = \\\\frac{y_2\\\\;-\\\\;y_1}{x_2\\\\;-\\\\;x_1} (x\\\\;-\\\\;x_2)$$<br>\r\nSubstituting the values, we get;<br>\r\n$$(y\\\\;-\\\\;0) = \\\\frac{5\\\\;-\\\\;0}{0\\\\;-\\\\;5} (x\\\\;-\\\\;5)$$<br>\r\n$$y = \\\\frac{5}{-5} (x\\\\;-\\\\;5)$$ <br>\r\n$$y = (\\\\;-\\\\;1)(x \\\\;\u2013\\\\; 5)$$<br>\r\n$$y = \\\\;-x + 5$$<br>\r\n$$x + y \\\\;\u2013 5 = 0$$<br>\r\nTherefore, the equation of a line passing through the given points $$(5,\\\\; 0)$$ and $$(0,\\\\; 5)$$ is $$x + y \\\\;\u2013\\\\; 5 = 0$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the slope of a line passing through the points $$(\\\\;-5,\\\\; 4)$$ and $$(3,\\\\; -2)$$.\",\n                    \"text\": \"What is the slope of a line passing through the points $$(\\\\;-5,\\\\; 4)$$ and $$(3,\\\\; -2)$$.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The slope of a straight line passing through the points $$(x_1,\\\\; y_1)$$ and $$(x_2,\\\\; y_2)$$ can be written as:<br>\r\nSlope $$= \\\\frac{y_2\\\\;-\\\\;y_1}{x_2\\\\;-\\\\;x_1}$$<br>\r\nSubstitute $$(x_1,\\\\; y_1) = (\\\\;-\\\\;5,\\\\; 4)$$ and $$(x_2,\\\\; y_2) = (3,\\\\; \\\\;-\\\\;2)$$<br>\r\nSlope $$= \\\\frac{-2\\\\;-\\\\;4}{3 + 5}  = \\\\frac{-3}{4}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{3}{4}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The slope of a straight line passing through the points $$(x_1,\\\\; y_1)$$ and $$(x_2,\\\\; y_2)$$ can be written as:<br>\r\nSlope $$= \\\\frac{y_2\\\\;-\\\\;y_1}{x_2\\\\;-\\\\;x_1}$$<br>\r\nSubstitute $$(x_1,\\\\; y_1) = (\\\\;-\\\\;5,\\\\; 4)$$ and $$(x_2,\\\\; y_2) = (3,\\\\; \\\\;-\\\\;2)$$<br>\r\nSlope $$= \\\\frac{-2\\\\;-\\\\;4}{3 + 5}  = \\\\frac{-3}{4}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{-4}{3}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The slope of a straight line passing through the points $$(x_1,\\\\; y_1)$$ and $$(x_2,\\\\; y_2)$$ can be written as:<br>\r\nSlope $$= \\\\frac{y_2\\\\;-\\\\;y_1}{x_2\\\\;-\\\\;x_1}$$<br>\r\nSubstitute $$(x_1,\\\\; y_1) = (\\\\;-\\\\;5,\\\\; 4)$$ and $$(x_2,\\\\; y_2) = (3,\\\\; \\\\;-\\\\;2)$$<br>\r\nSlope $$= \\\\frac{-2\\\\;-\\\\;4}{3 + 5}  = \\\\frac{-3}{4}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{4}{3}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The slope of a straight line passing through the points $$(x_1,\\\\; y_1)$$ and $$(x_2,\\\\; y_2)$$ can be written as:<br>\r\nSlope $$= \\\\frac{y_2\\\\;-\\\\;y_1}{x_2\\\\;-\\\\;x_1}$$<br>\r\nSubstitute $$(x_1,\\\\; y_1) = (\\\\;-\\\\;5,\\\\; 4)$$ and $$(x_2,\\\\; y_2) = (3,\\\\; \\\\;-\\\\;2)$$<br>\r\nSlope $$= \\\\frac{-2\\\\;-\\\\;4}{3 + 5}  = \\\\frac{-3}{4}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{-3}{4}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The slope of a straight line passing through the points $$(x_1,\\\\; y_1)$$ and $$(x_2,\\\\; y_2)$$ can be written as:<br>\r\nSlope $$= \\\\frac{y_2\\\\;-\\\\;y_1}{x_2\\\\;-\\\\;x_1}$$<br>\r\nSubstitute $$(x_1,\\\\; y_1) = (\\\\;-\\\\;5,\\\\; 4)$$ and $$(x_2,\\\\; y_2) = (3,\\\\; \\\\;-\\\\;2)$$<br>\r\nSlope $$= \\\\frac{-2\\\\;-\\\\;4}{3 + 5}  = \\\\frac{-3}{4}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The slope of a straight line passing through the points $$(x_1,\\\\; y_1)$$ and $$(x_2,\\\\; y_2)$$ can be written as:<br>\r\nSlope $$= \\\\frac{y_2\\\\;-\\\\;y_1}{x_2\\\\;-\\\\;x_1}$$<br>\r\nSubstitute $$(x_1,\\\\; y_1) = (\\\\;-\\\\;5,\\\\; 4)$$ and $$(x_2,\\\\; y_2) = (3,\\\\; \\\\;-\\\\;2)$$<br>\r\nSlope $$= \\\\frac{-2\\\\;-\\\\;4}{3 + 5}  = \\\\frac{-3}{4}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the equation of a vertical line passing through the point $$A (\\\\;-3,\\\\; \\\\;-5)$$?\",\n                    \"text\": \"What is the equation of a vertical line passing through the point $$A (\\\\;-3,\\\\; \\\\;-5)$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The equation of a vertical line passing through the point $$(a,\\\\; b)$$ is $$x = a$$.<br>\r\nThe equation of a vertical line passing through the point $$A\\\\; (\\\\;-3,\\\\; -5)$$ is  $$x = \\\\;-3$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$y = \\\\;-5$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The equation of a vertical line passing through the point $$(a,\\\\; b)$$ is $$x = a$$.<br>\r\nThe equation of a vertical line passing through the point $$A\\\\; (\\\\;-3,\\\\; -5)$$ is  $$x = \\\\;-3$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$x = 3$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The equation of a vertical line passing through the point $$(a,\\\\; b)$$ is $$x = a$$.<br>\r\nThe equation of a vertical line passing through the point $$A\\\\; (\\\\;-3,\\\\; -5)$$ is  $$x = \\\\;-3$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\;-3x\\\\;-\\\\;5y = 0$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The equation of a vertical line passing through the point $$(a,\\\\; b)$$ is $$x = a$$.<br>\r\nThe equation of a vertical line passing through the point $$A\\\\; (\\\\;-3,\\\\; -5)$$ is  $$x = \\\\;-3$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$x = \\\\;-3$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The equation of a vertical line passing through the point $$(a,\\\\; b)$$ is $$x = a$$.<br>\r\nThe equation of a vertical line passing through the point $$A\\\\; (\\\\;-3,\\\\; -5)$$ is  $$x = \\\\;-3$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The equation of a vertical line passing through the point $$(a,\\\\; b)$$ is $$x = a$$.<br>\r\nThe equation of a vertical line passing through the point $$A\\\\; (\\\\;-3,\\\\; -5)$$ is  $$x = \\\\;-3$$.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"12-frequently-asked-questions-on-two-point-form\">Frequently Asked Questions On Two Point Form<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-c3a71426-1039-416b-91a9-b0e252f803c1\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-c3a71426-1039-416b-91a9-b0e252f803c1\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-c3a71426-1039-416b-91a9-b0e252f803c1\"><strong>How do you determine whether a point lies on a line?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-c3a71426-1039-416b-91a9-b0e252f803c1\">\n\n<p class=\"eplus-wrapper\">Every point on a line satisfies its line equation. For example, to see whether (3, 6) lies on a line $y = 2x$, we substitute $x = 3$ and $y = 6$ in the given equation. Then we get: $6 = 2(3)$ or, $6 = 6$. The equation is satisfied and hence the point (3, 6) lies on the line $y = 2x$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-c3a71426-1039-416b-91a9-b0e252f803c1\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-c3a71426-1039-416b-91a9-b0e252f803c1\"><strong>What is the point slope form?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-c3a71426-1039-416b-91a9-b0e252f803c1\">\n\n<p class=\"eplus-wrapper\">The equation of line in point slope form is given by $y \\;-\\; y_1 = m (x \\;-\\; x_1)$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-c3a71426-1039-416b-91a9-b0e252f803c1\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-c3a71426-1039-416b-91a9-b0e252f803c1\"><strong>What is the equation of x-axis?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-c3a71426-1039-416b-91a9-b0e252f803c1\">\n\n<p class=\"eplus-wrapper\">The equation of x-axis is $y = 0$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-c3a71426-1039-416b-91a9-b0e252f803c1\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-c3a71426-1039-416b-91a9-b0e252f803c1\"><strong>What is the equation of y-axis?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-c3a71426-1039-416b-91a9-b0e252f803c1\">\n\n<p class=\"eplus-wrapper\">The equation of y-axis is x = 0.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is Two Point Form in Math? Two point form in math is one of the important methods to find the equation of a line when coordinates of any two points on the line are known. The equation of a line is used to represent each and every point on the line, we can say &#8230; <a title=\"Two Point Form \u2013 Definition, Derivation, Formula, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/two-point-form\" aria-label=\"More on Two Point Form \u2013 Definition, Derivation, Formula, Examples\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-27282","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27282","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=27282"}],"version-history":[{"count":12,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27282\/revisions"}],"predecessor-version":[{"id":35724,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27282\/revisions\/35724"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=27282"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=27282"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=27282"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}