{"id":27644,"date":"2023-04-17T09:06:55","date_gmt":"2023-04-17T09:06:55","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=27644"},"modified":"2024-02-05T15:39:33","modified_gmt":"2024-02-05T15:39:33","slug":"finding-slope-of-line-from-two-points-formula-example","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/finding-slope-from-two-points","title":{"rendered":"Finding Slope of Line from Two Points: Formula, Example"},"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-466192cd-0264-48cf-a918-3908136a93c1\" 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\/finding-slope-from-two-points#0-what-is-finding-slope-from-two-points>What Is Finding Slope from Two Points?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/finding-slope-from-two-points#1-finding-slope-from-two-points-formula>Finding Slope from Two Points Formula<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/finding-slope-from-two-points#2-derivation-of-the-formula-for-finding-slope-from-two-points>Derivation of the Formula for Finding Slope from Two Points<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/finding-slope-from-two-points#6-solved-examples-on-finding-slope-from-two-points>Solved Examples on Finding Slope From Two Points<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/finding-slope-from-two-points#7-practice-problems-on-finding-slope-from-two-points>Practice Problems on Finding Slope from Two Points<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/finding-slope-from-two-points#8-frequently-asked-questions-on-finding-slope-from-two-points>Frequently Asked Questions on Finding Slope from Two Points<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-finding-slope-from-two-points\">What Is Finding Slope from Two Points?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Finding slope from two points refers to finding the slope of a line when coordinates of two points on the line are given. The slope of a line is the measurement of the change in vertical distance over the change in the horizontal distance (rise-over-run ratio)<\/strong>. Slope tells us how steep a straight line is.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The slope can be calculated by applying different formulas based on the given information about the line. When coordinates of two points on the line are given, then we use the formula for finding the slope from two points. Let us discuss its formula.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"832\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rise-and-run-calculated-from-coordinates-of-two-points.png\" alt=\"Rise and run calculated from coordinates of two points\" class=\"wp-image-35688\" title=\"Rise and run calculated from coordinates of two points\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rise-and-run-calculated-from-coordinates-of-two-points.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rise-and-run-calculated-from-coordinates-of-two-points-224x300.png 224w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\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-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\/addition-word-problems-on-finding-the-total\" 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_to_scenario_pt.png\" alt=\"Addition Word Problems on Finding the Total 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\">Addition Word Problems on Finding the Total 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\/arrange-the-decimal-numbers-from-smallest-to-greatest\" 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_order_dec_2_pt.png\" alt=\"Arrange the Decimal Numbers From Smallest to Greatest 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\">Arrange the Decimal Numbers From Smallest to Greatest 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\/complete-the-multiplication-of-two-2-digit-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\/mult_div_pv_complete_mult_1_pt.png\" alt=\"Complete the Multiplication of Two 2-Digit 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\">Complete the Multiplication of Two 2-Digit 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\/compose-objects-from-shapes\" 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\/geometry_compose_shapes_pt.png\" alt=\"Compose Objects from Shapes 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\">Compose Objects from Shapes 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\/connect-the-number-stars-from-1-to-10\" 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\/num_seq_starry_sky_8_gm.png\" alt=\"Connect the Number Stars from 1 to 10 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\">Connect the Number Stars from 1 to 10 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\/connect-the-number-stars-from-1-to-3\" 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\/num_seq_starry_sky_3_gm.png\" alt=\"Connect the Number Stars from 1 to 3 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\">Connect the Number Stars from 1 to 3 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\/connect-the-number-stars-from-1-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\/num_seq_starry_sky_4_gm.png\" alt=\"Connect the Number Stars from 1 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\">Connect the Number Stars from 1 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><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 = 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     checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-finding-slope-from-two-points-formula\">Finding Slope from Two Points Formula<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">As we discussed, the slope is defined by the rise-over-run formula.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Slope $= m = \\frac{\\Delta y}{\\Delta x} = \\frac{Change\\; in\\; y}{Change\\; in\\; x}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">If a line passes through two points A and B whose coordinates are $(x_1,\\; y_1)$ and $(x_2,\\; y_2)$, then the slope formula is given by<\/p>\n\n\n\n<p class=\"eplus-wrapper\">slope $= m = \\frac{Rise}{Run} = \\frac{\\Delta y}{\\Delta x} = \\frac{y_2-y_1}{x_2-x_1}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$m =$ slope of the line<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x_1 =$ the x-coordinate of the point A<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$y_1 =$ the y-coordinate of the point A<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x_2 =$ the x-coordinate of the point B<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$y_2 =$ the x-coordinate of the point B<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"665\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/finding-slope-from-two-points-rise-and-run.png\" alt=\"Finding slope from two points - rise and run\" class=\"wp-image-35689\" title=\"Finding slope from two points - rise and run\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/finding-slope-from-two-points-rise-and-run.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/finding-slope-from-two-points-rise-and-run-280x300.png 280w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\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 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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-derivation-of-the-formula-for-finding-slope-from-two-points\">Derivation of the Formula for Finding Slope from Two Points<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Let $\\theta$ be the angle formed by the line with the positive direction of the x-axis.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let $A\\;(x_1,\\; y_1)$ and $B\\;(x_2,\\; y_2)$ be two points on the line. Draw a horizontal and vertical line through the points A and B that intersect at C.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"696\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/calculating-slope-from-two-points-derivation.png\" alt=\"Calculating slope from two points derivation\" class=\"wp-image-35691\" title=\"Calculating slope from two points derivation\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/calculating-slope-from-two-points-derivation.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/calculating-slope-from-two-points-derivation-267x300.png 267w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">As we know if a line makes angle \u03b8 with the positive x-axis in the anticlockwise direction, then its slope is given by&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Slope $= m = tan\\; \\theta$ \u2026(i)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Also, from the above figure, $\\angle A = \\theta$ (corresponding angle)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, in triangle ABC,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$tan\\theta = \\frac{Opposite\\;side}{Adjacent\\;side} = \\frac{BC}{AC}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow tan\\theta = \\frac{y_2-y_1}{x_2-x_1}$ \u2026(ii)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">From equation (i) and (ii), we get the formula\/equation for finding slope with two points $(x_1,\\; y_1)$ and $(x_2,\\; y_2)$ on the line as<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$m = \\frac{y_2-y_1}{x_2-x_1}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-how-to-find-slope-from-two-points\">How to Find Slope from Two Points<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s look at the steps for finding slope from two points.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Use $(x_1,\\; y_1)$ to identify the first point.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Use $(x_2,\\; y_2)$ to identify the second point.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Find $(y_2- y_1)$, the difference between y-coordinates, and $(x_2- x_1)$, the difference between the x-coordinates.&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">To find the slope (m), divide the difference between y-coordinates by the difference between x-coordinates.&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">$m = \\frac{y_2- y_1}{x_2- x_1}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Note:<\/strong> While finding the slope, we can interchange points without affecting the result. The order of the points does not matter.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;$m = \\frac{y_1- y_2}{x_1- x_2} = \\frac{y_2- y_1}{x_2- x_1}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-facts-about-finding-slope-from-two-points\">Facts about Finding Slope from Two Points<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The slope is also known as \u201cgradient.\u201d<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The slope of a vertical line is undefined.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The slope of any horizontal line is zero.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">For the line having a positive slope, the rise-over-run ratio is always positive.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">For the line having a negative slope, the rise-over-run ratio is always negative.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The slope of parallel lines is equal. $(m_1 = m_2)$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The slopes of two perpendicular lines are negative reciprocals of each other. $(m_1 = \\frac{-1}{m_2})$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">If the three points A, B, and C are collinear, then&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">slope of $AB =$ slope of $BC =$ slope of AC<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In this article, we have learned about finding slopes with two points, its formula, derivation, steps of finding slopes from two points. Let\u2019s solve a few examples for better understanding.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-solved-examples-on-finding-slope-from-two-points\">Solved Examples on Finding Slope From Two Points<\/h2>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Calculate the slope of a line passing through the points <\/strong>$P(\\;\u20131,\\; 3)$<strong> and <\/strong>$Q(2,\\; 15)$<strong>.<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The line passes through the points $P(\\;\u20131,\\; 3)$ and $Q(2,\\; 15)$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(x_1,\\; y_1) = (\\;\u20131,\\; 3)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(x_2,\\; y_2) = (2,\\; 15)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Slope of line $PQ = m = \\frac{y_2-y_1}{x_2-x_1} = \\frac{15 &#8211; 3}{2 \\;-(\\;-1)} = \\frac{12}{3} = 4$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, the slope of the line PQ is 4.<\/p>\n\n\n\n<ol start=\"2\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>What is the slope of a line if rise <\/strong>$= 100$<strong> inches and run <\/strong>$= 25$<strong> feet?<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Rise $= 100$ inches<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Run $= 25$ feet $= 25\\times12 = 300$ inches (1 foot $= 12$ inches)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, slope $= \\frac{Rise}{Run} = \\frac{100}{300} = \\frac{1}{3}$<\/p>\n\n\n\n<ol start=\"3\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>If the slope of the line joining two points <\/strong>$(\\;\u20131,\\; 2k)$<strong> and <\/strong>$(\\;\u20132,\\; k+2)$<strong> is <\/strong>$\u20132$<strong>, then find the value of k.<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Slope of the line $= \u20132$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The line passes through the points $(\\;\u20131,\\; 2k)$ and $(\u2013\\;2,\\; k+2)$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(x_1,\\; y_2) = (\\;\u20131,\\; 2k)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(x_2,\\; y_2) = (\\;\u20132,\\; k + 2)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Slope $= \\frac{y_2-y_1}{x_2-x_1}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow -2 = \\frac{k + 2 &#8211; 2k}{\\;-2\\;-(\\;-1)}= \\frac{-\\;k+2}{-\\;1}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow -k + 2 = 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow k = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, the value of k is 0.<\/p>\n\n\n\n<ol start=\"4\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>If the three points A(2, 3), B(4, 0) and C(6, k) are collinear, find k.<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Given points are $A\\;(2,\\; 3),\\; B\\;(4,\\; 0)$ and $C\\;(6,\\; k)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For collinearity of three points A, B, and C, we write&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Slope of AB $=$ Slope of BC<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow \\frac{0-3}{4-2} = \\frac{k-0}{6-4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow \\\\frac{-3}{2} = \\frac{k}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow k = -3$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, three points $A\\;(2,\\; 3),\\; B\\;(4,\\; 0)$ and $C\\;(6,\\; k)$ are collinear for $k=-3$.<\/p>\n\n\n\n<ol start=\"5\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Derive the condition for zero slopes from two points <\/strong>$(x_1,\\; y_1)$<strong> and <\/strong>$(x_2,\\; y_2)$<strong>.<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Given points are $(x_1,\\; y_1)$ and $(x_2,\\; y_2)$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The slope of line $= \\frac{y_2-y_1}{x_2-x_1} = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For zero slope,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{y_2-y_1}{x_2-x_1} = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow y_2\\;-\\;y_1 = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow y_2 = y_1$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, the condition for zero slopes is $y_2 = y_1$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">If y-coordinates are the same, we get a horizontal line whose slope is always 0.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-practice-problems-on-finding-slope-from-two-points\">Practice Problems on Finding Slope from Two Points<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Finding Slope of Line from Two Points: Formula, Example<\/h2><p style=\"display:none;\">Attend this quiz & Test your knoweldge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">What is the slope of a line passing through the two points $(x_1,\\;y_1)$ and $(x_2,\\;y_2)$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{y_2-y_1}{x_2-x_1}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{x_2-x_1}{y_2-y_1}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{y_2+y_1}{x_2+x_1}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above<\/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: $\\frac{y_2-y_1}{x_2-x_1}$<br\/>The slope of a line passing through the two points $(x_1,\\;y_1)$ and $(x_2,\\;y_2)$ is given by<br>\r\n$m = \\frac{y_2-y_1}{x_2-x_1}$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Which of the following formulas are used to find the slope of a line?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$m = tan\\theta$ <\/div><div class=\"spq_answer_block\" data-value=\"1\">$m = \\frac{y_2-y_1}{x_2-x_1}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$m = \\frac{\\Delta\\;y}{\\Delta\\;x}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">All of the above<\/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: All of the above<br\/>All of the given formulas in options (a), (b), and (c) are used to find the slope of the line.<\/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\">The slope of a _______ is zero.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">horizontal lines<\/div><div class=\"spq_answer_block\" data-value=\"1\">vertical lines<\/div><div class=\"spq_answer_block\" data-value=\"2\">parallel lines<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of these<\/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: horizontal lines<br\/>The slope of a horizontal line is zero.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">The slope of a line joining two points (4, 6) and (2, 8) is<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$1$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$-1$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$2$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$-1$<\/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: $1$<br\/>The line passes through the points $(4,\\;6)$ and $(2,\\;8)$.<br>\r\nThe slope of line $= \\frac{y_2-y_1}{x_2-x_1} = \\frac{8-6}{2-4} = \\frac{2}{-2} =\\;-1$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">What is the value of k for which the points (3, 2) and (4, k) lie on a horizontal line?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1<\/div><div class=\"spq_answer_block\" data-value=\"1\">2<\/div><div class=\"spq_answer_block\" data-value=\"2\">3<\/div><div class=\"spq_answer_block\" data-value=\"3\">4<\/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: 2<br\/>For a horizontal line, the slope $= 0$<br>\r\n$\\Rightarrow \\frac{k-2}{4-3} = 0$<br>\r\n$\\Rightarrow k\\;-\\;2 = 0$<br>\r\n$\\Rightarrow $k = 2$<\/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 knoweldge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Finding Slope of Line from Two Points: Formula, Example\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Finding Slope of Line from Two Points\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the slope of a line passing through the two points $$(x_1,\\\\;y_1)$$ and $$(x_2,\\\\;y_2)$$?\",\n                    \"text\": \"What is the slope of a line passing through the two points $$(x_1,\\\\;y_1)$$ and $$(x_2,\\\\;y_2)$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The slope of a line passing through the two points $$(x_1,\\\\;y_1)$$ and $$(x_2,\\\\;y_2)$$ is given by<br>\r\n$$m = \\\\frac{y_2-y_1}{x_2-x_1}$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{x_2-x_1}{y_2-y_1}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The slope of a line passing through the two points $$(x_1,\\\\;y_1)$$ and $$(x_2,\\\\;y_2)$$ is given by<br>\r\n$$m = \\\\frac{y_2-y_1}{x_2-x_1}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{y_2+y_1}{x_2+x_1}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The slope of a line passing through the two points $$(x_1,\\\\;y_1)$$ and $$(x_2,\\\\;y_2)$$ is given by<br>\r\n$$m = \\\\frac{y_2-y_1}{x_2-x_1}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The slope of a line passing through the two points $$(x_1,\\\\;y_1)$$ and $$(x_2,\\\\;y_2)$$ is given by<br>\r\n$$m = \\\\frac{y_2-y_1}{x_2-x_1}$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{y_2-y_1}{x_2-x_1}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The slope of a line passing through the two points $$(x_1,\\\\;y_1)$$ and $$(x_2,\\\\;y_2)$$ is given by<br>\r\n$$m = \\\\frac{y_2-y_1}{x_2-x_1}$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The slope of a line passing through the two points $$(x_1,\\\\;y_1)$$ and $$(x_2,\\\\;y_2)$$ is given by<br>\r\n$$m = \\\\frac{y_2-y_1}{x_2-x_1}$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following formulas are used to find the slope of a line?\",\n                    \"text\": \"Which of the following formulas are used to find the slope of a line?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"All of the given formulas in options (a), (b), and (c) are used to find the slope of the line.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$m = tan\\\\theta$$ \",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"All of the given formulas in options (a), (b), and (c) are used to find the slope of the line.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$m = \\\\frac{y_2-y_1}{x_2-x_1}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"All of the given formulas in options (a), (b), and (c) are used to find the slope of the line.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$m = \\\\frac{\\\\Delta\\\\;y}{\\\\Delta\\\\;x}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"All of the given formulas in options (a), (b), and (c) are used to find the slope of the line.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"All of the above\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"All of the given formulas in options (a), (b), and (c) are used to find the slope of the line.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"All of the given formulas in options (a), (b), and (c) are used to find the slope of the line.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The slope of a _______ is zero.\",\n                    \"text\": \"The slope of a _______ is zero.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The slope of a horizontal line is zero.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"vertical lines\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The slope of a horizontal line is zero.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"parallel lines\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The slope of a horizontal line is zero.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of these\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The slope of a horizontal line is zero.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"horizontal lines\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The slope of a horizontal line is zero.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The slope of a horizontal line is zero.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The slope of a line joining two points (4, 6) and (2, 8) is\",\n                    \"text\": \"The slope of a line joining two points (4, 6) and (2, 8) is\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The line passes through the points $$(4,\\\\;6)$$ and $$(2,\\\\;8)$$.<br>\r\nThe slope of line $$= \\\\frac{y_2-y_1}{x_2-x_1} = \\\\frac{8-6}{2-4} = \\\\frac{2}{-2} =\\\\;-1$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$-1$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The line passes through the points $$(4,\\\\;6)$$ and $$(2,\\\\;8)$$.<br>\r\nThe slope of line $$= \\\\frac{y_2-y_1}{x_2-x_1} = \\\\frac{8-6}{2-4} = \\\\frac{2}{-2} =\\\\;-1$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The line passes through the points $$(4,\\\\;6)$$ and $$(2,\\\\;8)$$.<br>\r\nThe slope of line $$= \\\\frac{y_2-y_1}{x_2-x_1} = \\\\frac{8-6}{2-4} = \\\\frac{2}{-2} =\\\\;-1$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$-1$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The line passes through the points $$(4,\\\\;6)$$ and $$(2,\\\\;8)$$.<br>\r\nThe slope of line $$= \\\\frac{y_2-y_1}{x_2-x_1} = \\\\frac{8-6}{2-4} = \\\\frac{2}{-2} =\\\\;-1$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$1$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The line passes through the points $$(4,\\\\;6)$$ and $$(2,\\\\;8)$$.<br>\r\nThe slope of line $$= \\\\frac{y_2-y_1}{x_2-x_1} = \\\\frac{8-6}{2-4} = \\\\frac{2}{-2} =\\\\;-1$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The line passes through the points $$(4,\\\\;6)$$ and $$(2,\\\\;8)$$.<br>\r\nThe slope of line $$= \\\\frac{y_2-y_1}{x_2-x_1} = \\\\frac{8-6}{2-4} = \\\\frac{2}{-2} =\\\\;-1$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the value of k for which the points (3, 2) and (4, k) lie on a horizontal line?\",\n                    \"text\": \"What is the value of k for which the points (3, 2) and (4, k) lie on a horizontal line?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"For a horizontal line, the slope $$= 0$$<br>\r\n$$\\\\Rightarrow \\\\frac{k-2}{4-3} = 0$$<br>\r\n$$\\\\Rightarrow k\\\\;-\\\\;2 = 0$$<br>\r\n$$\\\\Rightarrow $$k = 2$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"For a horizontal line, the slope $$= 0$$<br>\r\n$$\\\\Rightarrow \\\\frac{k-2}{4-3} = 0$$<br>\r\n$$\\\\Rightarrow k\\\\;-\\\\;2 = 0$$<br>\r\n$$\\\\Rightarrow $$k = 2$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"For a horizontal line, the slope $$= 0$$<br>\r\n$$\\\\Rightarrow \\\\frac{k-2}{4-3} = 0$$<br>\r\n$$\\\\Rightarrow k\\\\;-\\\\;2 = 0$$<br>\r\n$$\\\\Rightarrow $$k = 2$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"For a horizontal line, the slope $$= 0$$<br>\r\n$$\\\\Rightarrow \\\\frac{k-2}{4-3} = 0$$<br>\r\n$$\\\\Rightarrow k\\\\;-\\\\;2 = 0$$<br>\r\n$$\\\\Rightarrow $$k = 2$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"2\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"For a horizontal line, the slope $$= 0$$<br>\r\n$$\\\\Rightarrow \\\\frac{k-2}{4-3} = 0$$<br>\r\n$$\\\\Rightarrow k\\\\;-\\\\;2 = 0$$<br>\r\n$$\\\\Rightarrow $$k = 2$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"For a horizontal line, the slope $$= 0$$<br>\r\n$$\\\\Rightarrow \\\\frac{k-2}{4-3} = 0$$<br>\r\n$$\\\\Rightarrow k\\\\;-\\\\;2 = 0$$<br>\r\n$$\\\\Rightarrow $$k = 2$$\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-frequently-asked-questions-on-finding-slope-from-two-points\">Frequently Asked Questions on Finding Slope from Two Points<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-94159774-3efb-45a4-8722-7a7fb8498e91\" 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-0-94159774-3efb-45a4-8722-7a7fb8498e91\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-94159774-3efb-45a4-8722-7a7fb8498e91\"><strong>What Is the meaning of an undefined slope?<\/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-0-94159774-3efb-45a4-8722-7a7fb8498e91\">\n\n<p class=\"eplus-wrapper\">An undefined slope means a line making an angle of $90^\\circ$ with the positive direction of the x-axis.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">That means the line is a vertical line.<\/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-1-94159774-3efb-45a4-8722-7a7fb8498e91\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-94159774-3efb-45a4-8722-7a7fb8498e91\"><strong>What is the use of slope in real life?<\/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-1-94159774-3efb-45a4-8722-7a7fb8498e91\">\n\n<p class=\"eplus-wrapper\">There are numerous applications for slopes (or gradients) in everyday life. Every hill has a slope, and the steeper the hill, the greater its gradient. This is one of the most obvious physical examples.<\/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-2-94159774-3efb-45a4-8722-7a7fb8498e91\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-94159774-3efb-45a4-8722-7a7fb8498e91\"><strong>What does a negative slope signify?<\/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-2-94159774-3efb-45a4-8722-7a7fb8498e91\">\n\n<p class=\"eplus-wrapper\">The negative slope signifies that a line declines downwards as we move from left to right. Also graphically, y decreases as x increases.<\/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-3-94159774-3efb-45a4-8722-7a7fb8498e91\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-94159774-3efb-45a4-8722-7a7fb8498e91\"><strong>What is the formula for finding the slope from two points?<\/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-3-94159774-3efb-45a4-8722-7a7fb8498e91\">\n\n<p class=\"eplus-wrapper\">The formula for finding the slope from two points $(x_1,\\; y_1)$ and $(x_2,\\; y_2)$ is $\\frac{y_2-y_1}{x_2-x_1}$.<\/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-4-94159774-3efb-45a4-8722-7a7fb8498e91\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-94159774-3efb-45a4-8722-7a7fb8498e91\"><strong>How can we find slope with two points?<\/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-4-94159774-3efb-45a4-8722-7a7fb8498e91\">\n\n<p class=\"eplus-wrapper\">To find the slope with two points, apply two point slope formula $m = \\frac{y_2-y_1}{x_2-x_1}$.<\/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-5-94159774-3efb-45a4-8722-7a7fb8498e91\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-94159774-3efb-45a4-8722-7a7fb8498e91\"><strong>What is the method to find the slope of a line from the graph?<\/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-5-94159774-3efb-45a4-8722-7a7fb8498e91\">\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Denote a single random point on it with $(x_1,\\; y_1)$.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Denote another point on it with $(x_2,\\; y_2)$.<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">Use the formula: The slope of line $= \\frac{y_2-y_1}{x_2-x_1}$.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is Finding Slope from Two Points? Finding slope from two points refers to finding the slope of a line when coordinates of two points on the line are given. The slope of a line is the measurement of the change in vertical distance over the change in the horizontal distance (rise-over-run ratio). Slope tells &#8230; <a title=\"Finding Slope of Line from Two Points: Formula, Example\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/finding-slope-from-two-points\" aria-label=\"More on Finding Slope of Line from Two Points: Formula, Example\">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-27644","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\/27644","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=27644"}],"version-history":[{"count":11,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27644\/revisions"}],"predecessor-version":[{"id":39944,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27644\/revisions\/39944"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=27644"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=27644"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=27644"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}