{"id":36071,"date":"2023-11-10T22:09:00","date_gmt":"2023-11-10T22:09:00","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=36071"},"modified":"2023-11-16T11:41:31","modified_gmt":"2023-11-16T11:41:31","slug":"point-slope-form","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/point-slope-form","title":{"rendered":"Point Slope Form: Definition, Derivation, Facts, Examples, FAQs"},"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-ee617fee-9957-47a2-a6e3-291b6d60ae4c\" 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\/point-slope-form#0-what-is-point-slope-form>What Is Point Slope Form?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/point-slope-form#1-point-slope-formula>Point Slope Formula<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/point-slope-form#2-derivation-of-point-slope-formula>Derivation of Point Slope Formula<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/point-slope-form#7-solved-examples-on-point-slope-form>Solved Examples on Point Slope Form<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/point-slope-form#8-practice-problems-on-point-slope-form>Practice Problems on Point Slope Form<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/point-slope-form#9-frequently-asked-questions-about-point-slope-form>Frequently Asked Questions about Point Slope Form<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-point-slope-form\">What Is Point Slope Form?<\/h2>\n\n\n\n<p><strong>The point slope form of the equation of a line refers to the equation of a line with slope m and passing through the point with coordinates (x<sub>1<\/sub>, y<strong><sub>1<\/sub><\/strong>). It can be given as<\/strong><\/p>\n\n\n\n<p>(y \u2212 y<strong><sub>1<\/sub><\/strong>) = m(x \u2212 x<strong><sub>1<\/sub><\/strong>)<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"493\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/understanding-the-point-slope-form-of-a-line.png\" alt=\"Understanding the point slope form of a line\" class=\"wp-image-36076\" title=\"Understanding the point slope form of a line\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/understanding-the-point-slope-form-of-a-line.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/understanding-the-point-slope-form-of-a-line-300x239.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>We can write the equation of a line using different forms such as slope-intercept form, two-point form, etc., based on the information known to us. The point slope form, as the name suggests, uses the slope of the line and the coordinates of any point lying on the line to define the equation of the line.<\/p>\n\n\n\n<p><strong>What is a Slope?<\/strong><\/p>\n\n\n\n<p>The slope or the gradient of a line is denoted by m. It tells us about the steepness of a line. It is defined by the rise over run ratio.&nbsp;<\/p>\n\n\n\n<p>If a line passes through the points (x<strong><sub>1<\/sub><\/strong>, y<strong><sub>1<\/sub><\/strong>) and (x<strong><sub>2<\/sub><\/strong>, y<strong><sub>2<\/sub><\/strong>), its slope can be defined as<\/p>\n\n\n\n<p>Slope $= m = \\frac{Rise}{Run} = \\frac{Change\\; in\\; y}{Change\\; in\\; x} = \\frac{(y2 \u2212 y_{1})}{(x2 \u2212 x_{1})}$<\/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\" 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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 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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 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});\n    <\/script><h2 class=\"wp-block-heading\" id=\"1-point-slope-formula\">Point Slope Formula<\/h2>\n\n\n\n<p>The point slope form formula of the equation of a straight line is given by&nbsp;<\/p>\n\n\n\n<p>(y \u2212 y<sub>1<\/sub>)= m(x \u2212 x<sub>1<\/sub>)\u00a0<\/p>\n\n\n\n<p>where,<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(x, y) represents the coordinates of any point on the line.<\/li>\n\n\n\n<li>(x<sub>1<\/sub>, y<sub>1<\/sub>) represents the coordinates of a given fixed point on the line.<\/li>\n\n\n\n<li>m is the slope of the line.<\/li>\n<\/ul>\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\/color-animals-and-trace-word-forms-within-10\" data-vars-ga-category=\"splashlearn_vocab\" 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Trace Word Forms (Within 5)\">\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\/color-flowers-and-trace-word-forms-within-10\" 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\/color-flowers-and-trace-word-forms-within-10.jpeg\" alt=\"Color Flowers and Trace Word Forms (Within 10)\">\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\/color-flowers-and-trace-word-forms-within-5\" 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\/color-flowers-and-trace-word-forms-within-5.jpeg\" alt=\"Color Flowers and Trace Word Forms (Within 5)\">\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\/color-food-items-and-trace-word-forms-within-10\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div 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Trace Word Forms (Within 5)\">\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 = 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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\" id=\"2-derivation-of-point-slope-formula\">Derivation of Point Slope Formula<\/h2>\n\n\n\n<p>Let us consider a line with slope m . Assume that (x<sub>1<\/sub>, y<sub>1<\/sub>) is a fixed and known point on the line and (x, y) is just an ordinary point.\u00a0<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"696\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/derivation-of-the-point-slope-formula.png\" alt=\"Derivation of the point slope formula\" class=\"wp-image-36078\" title=\"Derivation of the point slope formula\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/derivation-of-the-point-slope-formula.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/derivation-of-the-point-slope-formula-267x300.png 267w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Let\u2019s understand how to find m in point slope form. We know that the formula for the slope of a line passing through the points (x<sub>1<\/sub>, y<sub>1<\/sub>) and (x<sub>2<\/sub>, y<sub>2<\/sub>) is given by<\/p>\n\n\n\n<p>Slope $= m = \\frac{Rise}{Run} = \\frac{Change \\;in\\; y}{Change \\;in\\; x} = \\frac{(y2 \u2212 y_{1})}{(x2 \u2212 x_{1})}$<\/p>\n\n\n\n<p>Suppose that we know the coordinates of only one point (x<sub>1<\/sub>, y<sub>1<\/sub>). Let the coordinates of the other random point on the line be (x, y). We can rewrite the formula for the slope with one point as<\/p>\n\n\n\n<p>$\\Rightarrow m = \\frac{(y \u2212 y_{1})}{(x \u2212 x_{1})}$<\/p>\n\n\n\n<p>On cross multiplication, we get the point-slope formula as<\/p>\n\n\n\n<p>(y \u2212 y<sub>1<\/sub>) = m(x \u2212 x<sub>1<\/sub>)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-equation-of-a-line-with-slope-and-coordinates-of-a-point\">Equation of a Line with Slope and Coordinates of a Point<\/h2>\n\n\n\n<p>We can find the equation of a line with slope m and coordinates of a point (x<sub>1<\/sub>, y<sub>1<\/sub>) using the point slope formula.<\/p>\n\n\n\n<p><strong>Example: <\/strong>Find the equation of a line with slope \u22122 such that the point is (2, 3) lies on the line.\u00a0<\/p>\n\n\n\n<p>Here, (x<sub>1<\/sub>, y<sub>1<\/sub>) = (2, 3) is the point on the line.<\/p>\n\n\n\n<p>m = \u22122 is the slope.<\/p>\n\n\n\n<p>Using the point slope form, we get&nbsp;<\/p>\n\n\n\n<p>(y \u2212 y<sub>1<\/sub>) = m(x \u2212 x<sub>1<\/sub>)<\/p>\n\n\n\n<p>(y \u2212 3) = (\u2212 2)(x \u2212 2))<\/p>\n\n\n\n<p>y\u2212 3 = \u22122x + 4<\/p>\n\n\n\n<p>y = (\u2212 2)x + 7<\/p>\n\n\n\n<p>\\Rightarrow 2x + y = 7<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-deriving-two-point-form-using-point-slope-form\">Deriving Two Point Form Using Point Slope Form<\/h2>\n\n\n\n<p>Consider a case where the slope of the line is not given. We only know the coordinates of two points on the line. Let the two points be (x<sub>1<\/sub>, y<sub>1<\/sub>) and\u00a0 (x<sub>2<\/sub>, y<sub>2<\/sub>).\u00a0<\/p>\n\n\n\n<p>In such a case, we will first find the slope by:<\/p>\n\n\n\n<p>$m = \\frac{(y_{2} \u2212 y_{1})}{(x_{2} \u2212 x_{1})}$<\/p>\n\n\n\n<p>Now that we know the slope of the line, we can find the the equation of a line by using the Point Slope Form (y \u2212 y<sub>1<\/sub>) = m(x \u2212 x<sub>1<\/sub>).\u00a0<\/p>\n\n\n\n<p>(<em>You can use the coordinates of any of the given two points here.<\/em>)<\/p>\n\n\n\n<p>(y \u2212 y<sub>1<\/sub>) = m(x \u2212 x<sub>1<\/sub>)<\/p>\n\n\n\n<p>(y \u2212 y<sub>1<\/sub>) $= \\frac{(y_{2} \u2212 y_{1})}{(x_{2} \u2212 x_{1})} (x \u2212 x_{1})$<\/p>\n\n\n\n<p>This is called two-point form.<\/p>\n\n\n\n<p><strong>Example: <\/strong>Find equation of a line where (\u2212 1, 2) and (3, 0) are two points on the line.<\/p>\n\n\n\n<p>The equation of the line is:<\/p>\n\n\n\n<p>\u00a0(y \u2212 0) $= \\frac{0 \u2212 2}{3\u2212 (\u2212 1)} (x \u2212 (\u2212 1))$<\/p>\n\n\n\n<p>$y = \\frac{\u2212 2}{3} (x + 1)$<\/p>\n\n\n\n<p>$\\Rightarrow 3y = \u22122x \u2212 2$<\/p>\n\n\n\n<p>$\\Rightarrow 2x \u2212 3y =  \u22122$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-facts-about-point-slope-form\">Facts about Point Slope Form<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>To find the equation of a line using the Point Slope Form, we must know the slope (or enough information to find the slope) and the coordinates of a fixed point on the line.<\/li>\n\n\n\n<li>The equation of a line in the standard form is given by ax + by = c, where a and b cannot be simultaneously 0.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned how to find the equation of a straight line using the slope point form. We discussed its formula, derivation by visualizing it on a graph, and examples. Let\u2019s check our understanding by solving a few examples and practice problems based on the Point Slope Form.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-solved-examples-on-point-slope-form\">Solved Examples on Point Slope Form<\/h2>\n\n\n\n<p><strong>1. Find the slope and equation of a line if the coordinates of two points on the line are <\/strong><strong>(0,-1)<\/strong><strong> and <\/strong><strong>(3,-5)<\/strong><strong>.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Let (x<sub>1<\/sub>, y<sub>1<\/sub>) = <strong>(0, \u22121)<\/strong> and (x<sub>2<\/sub>, y<sub>2<\/sub>) be <strong>(3, \u2212 5).\u00a0<\/strong><\/p>\n\n\n\n<p>Slope $(m) = \\frac{(y_{2} \u2212 y_{1})}{(x_{2} \u2212 x_{1})} = \\frac{\u2212 5\u2212 (\u2212 1)}{3 \u2212 0} = \\frac{\u2212 5 + 1}{3} = \\frac{\u2212 4}{3}$\u00a0<\/p>\n\n\n\n<p>Let\u2019s use (x<sub>1<\/sub>, y<sub>1<\/sub>) = <strong>(0, \u22121) <\/strong>and<strong> <\/strong>m $= \\frac{\u2212 4}{3}$ to find the equation of the line in the slope point form.<\/p>\n\n\n\n<p>(y \u2212 y<sub>1<\/sub>) = m(x \u2212 x<sub>1<\/sub>)<\/p>\n\n\n\n<p>$(y\u2212 (\u2212 1)) = \\frac{\u2212 4}{3}(x \u2212 0)$<\/p>\n\n\n\n<p>$(y + 1) = \\frac{\u2212 4}{3}x$<\/p>\n\n\n\n<p>3y + 3 = \u2212 4x<\/p>\n\n\n\n<p>4x + 3y = \u2212 3<\/p>\n\n\n\n<p><strong>2. Find the equation of a line passing through the point (3, 6) and has a slope <\/strong>$\u2212 \\frac{1}{2}$<strong>.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Slope $(m) = \u2212 \\frac{1}{2}$<\/p>\n\n\n\n<p>Let the fixed point be (x<sub>1<\/sub>, y<sub>1<\/sub>) = (3, 6).<\/p>\n\n\n\n<p>Point Slope Form: (y \u2212 y<sub>1<\/sub>) = m(x \u2212 x<sub>1<\/sub>)<\/p>\n\n\n\n<p>The equation of the line will be:&nbsp;<\/p>\n\n\n\n<p>(y \u2212 6) $= (\u2212 \\frac{1}{2}) (x \u2212 3)$<\/p>\n\n\n\n<p>2(y \u2212 6)= \u2212 1(x \u2212 3)<\/p>\n\n\n\n<p>2y \u2212 12 = \u2212 x + 3<\/p>\n\n\n\n<p>x + 2y = 15<\/p>\n\n\n\n<p><strong>3. What is the equation of a line with slope -5 and passing through the point (\u2212<\/strong> <strong>7, 1)?<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Slope (m) $= \u2212 \\frac{1}{2}$<\/p>\n\n\n\n<p>Let the fixed point be (3, 6).<\/p>\n\n\n\n<p>Point Slope Form: (y \u2212 y<sub>1<\/sub>) = m(x \u2212 x<sub>1<\/sub>)<\/p>\n\n\n\n<p>The equation of the line will be:&nbsp;<\/p>\n\n\n\n<p>(y \u2212 6) $= (\u2212 \\frac{1}{2})(x \\;-\\; 3)$<\/p>\n\n\n\n<p>2(y \u2212 6) = \u2212 1(x \u2212 3)<\/p>\n\n\n\n<p>2y \u2212 12 = \u2212 x + 3<\/p>\n\n\n\n<p>x + 2y = 15<\/p>\n\n\n\n<p><strong>4. Find the equation of a line passing through the points (2,\u2212 3) and (\u22121, 10).<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Let (x<sub>1<\/sub>, y<sub>1<\/sub>) = <strong>(2, \u2212<\/strong> <strong>3)<\/strong> and (x<sub>2<\/sub>, y<sub>2<\/sub>) be <strong>(\u22121, 10).<\/strong><\/p>\n\n\n\n<p>The point slope linear equation will be:<\/p>\n\n\n\n<p>\u00a0$(y \u2212 y_{1}) = \\frac{(y_{2} \u2212 y_{1})}{(x_{2} \u2212 x_{1})} (x \u2212 x_{1})$<\/p>\n\n\n\n<p>$(y\u2212 (\u2212 3)) = \\frac{(10\u2212 (\u2212 3))}{(\u2212 1 \u2212 2)}(x \u2212 2)$<\/p>\n\n\n\n<p>$y + 3 = \\frac{1}{3} \u22123(x \u2212 2)$<\/p>\n\n\n\n<p>\u2212 3(y + 3) = 13(x \u2212 2)<\/p>\n\n\n\n<p>\u2212 3y \u2212 9 = 13x \u2212 26<\/p>\n\n\n\n<p>13x + 3y = 17<\/p>\n\n\n\n<p><strong>5. What is the equation of a line with slope 0 and passing through the point (7, \u2212<\/strong> <strong>2)? What can you say about this line? Graph the line.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Let (x<sub>1<\/sub>, y<sub>1<\/sub>) = <strong>(7, \u2212<\/strong> <strong>2)<\/strong> and m = 0<strong>.<\/strong><\/p>\n\n\n\n<p>Point Slope Form: (y \u2212 y<sub>1<\/sub>) = m(x \u2212 x<sub>1<\/sub>)<\/p>\n\n\n\n<p>The point slope form equation of the line will be:<\/p>\n\n\n\n<p>\u00a0(y \u2212 (\u2212 2)) = 0 (x \u2212 7)<\/p>\n\n\n\n<p>(y\u2212 ( \u22122)) = 0<\/p>\n\n\n\n<p>y + 2 = 0<\/p>\n\n\n\n<p>y = \u22122<\/p>\n\n\n\n<p>As the slope of the line is 0, it is a horizontal line parallel to the x-axis. Also, since the equation of the line is y = \u22122, it is a horizontal line passing through the point (0, \u22122). The value of the y-coordinate y = \u22122 remains constant.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"397\" height=\"375\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/graph-of-the-line-y-2-line.png\" alt=\"Graph of the line y = -2 line\" class=\"wp-image-36079\" title=\"Graph of the line y = -2 line\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/graph-of-the-line-y-2-line.png 397w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/graph-of-the-line-y-2-line-300x283.png 300w\" sizes=\"auto, (max-width: 397px) 100vw, 397px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-practice-problems-on-point-slope-form\">Practice Problems on Point Slope Form<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Point Slope Form: Definition, Derivation, Facts, Examples, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">The point slope form of a line with slope m and passing through the point (a, b) can be written as<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$(y \u2212 y1) = m(x \u2212 x_{1})$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$(y \u2212 b) = m(x \u2212 a)$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$(x \u2212 b) = m(y \u2212 a)$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$(y \u2212 a) = m(x \u2212 b)$<\/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: $(y \u2212 b) = m(x \u2212 a)$<br\/>The point slope form of a line with slope m and passing through the point (a, b) can be written as (y \u2212 b) = m(x \u2212 a).<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">The line passing through the point (-1, 5) and with slope 0 is ___________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">parallel to the x-axis<\/div><div class=\"spq_answer_block\" data-value=\"1\">parallel to the y-axis<\/div><div class=\"spq_answer_block\" data-value=\"2\">pass through the origin<\/div><div class=\"spq_answer_block\" data-value=\"3\">perpendicular to the x-axis<\/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: parallel to the x-axis<br\/>Slope (m) = 0 and fixed point = (\u2212 1, 5)<br>\r\nEquation of a line is: y - 5 = 0(x \u2212 ( \u2212 1))<br>\r\n$y \u2212 5 = 0\\Rightarrow y = 5$<br>\r\nIt will be parallel to the x-axis.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">The equation of the line passing through the origin and with slope 0 is<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">x = 0<\/div><div class=\"spq_answer_block\" data-value=\"1\">y = 1<\/div><div class=\"spq_answer_block\" data-value=\"2\">x + y = \u2212 3<\/div><div class=\"spq_answer_block\" data-value=\"3\">y = 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: y = 0<br\/>Point = O = (0, 0) and slope = m = 0<br>\r\nPoint Slope Form: $(y \u2212 y_{1})= m(x \u2212 x_{1})$<br>\r\nEquation of line: (y \u2212 0) = 0(x \u2212 0)<br>\r\nEquation of line: y = 0<br>\r\nIt is the x-axis.<\/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 straight line passing through the points (3, 0) and (0, 3)?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">x \u2212 y = 3<\/div><div class=\"spq_answer_block\" data-value=\"1\">x + y = \u22123<\/div><div class=\"spq_answer_block\" data-value=\"2\">x + y = 3<\/div><div class=\"spq_answer_block\" data-value=\"3\">x \u2212 y = 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: x + y = 3<br\/>The equation of the line will be:<br>\r\n$(y \u2212 0) = \\frac{(3 \u2212 0)}{(0 \u2212 3)} (x \u2212 3)$<br>\r\n$y = \\frac{3}{\u22123}(x \u2212 3)$<br>\r\ny = \u22121(x \u2212 3)<br>\r\ny = \u2212x + 3<br>\r\nx + y = 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\": \"Point Slope Form: Definition, Derivation, Facts, Examples, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Point Slope Form\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The point slope form of a line with slope m and passing through the point (a, b) can be written as\",\n                    \"text\": \"The point slope form of a line with slope m and passing through the point (a, b) can be written as\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The point slope form of a line with slope m and passing through the point (a, b) can be written as (y \u2212 b) = m(x \u2212 a).\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(y \u2212 y1) = m(x \u2212 x_{1})$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The point slope form of a line with slope m and passing through the point (a, b) can be written as (y \u2212 b) = m(x \u2212 a).\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(x \u2212 b) = m(y \u2212 a)$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The point slope form of a line with slope m and passing through the point (a, b) can be written as (y \u2212 b) = m(x \u2212 a).\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(y \u2212 a) = m(x \u2212 b)$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The point slope form of a line with slope m and passing through the point (a, b) can be written as (y \u2212 b) = m(x \u2212 a).\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$(y \u2212 b) = m(x \u2212 a)$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The point slope form of a line with slope m and passing through the point (a, b) can be written as (y \u2212 b) = m(x \u2212 a).\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The point slope form of a line with slope m and passing through the point (a, b) can be written as (y \u2212 b) = m(x \u2212 a).\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The line passing through the point (-1, 5) and with slope 0 is ___________.\",\n                    \"text\": \"The line passing through the point (-1, 5) and with slope 0 is ___________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Slope (m) = 0 and fixed point = (\u2212 1, 5)<br>\r\nEquation of a line is: y - 5 = 0(x \u2212 ( \u2212 1))<br>\r\n$$y \u2212 5 = 0\\\\Rightarrow y = 5$$<br>\r\nIt will be parallel to the x-axis.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"parallel to the y-axis\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Slope (m) = 0 and fixed point = (\u2212 1, 5)<br>\r\nEquation of a line is: y - 5 = 0(x \u2212 ( \u2212 1))<br>\r\n$$y \u2212 5 = 0\\\\Rightarrow y = 5$$<br>\r\nIt will be parallel to the x-axis.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"pass through the origin\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Slope (m) = 0 and fixed point = (\u2212 1, 5)<br>\r\nEquation of a line is: y - 5 = 0(x \u2212 ( \u2212 1))<br>\r\n$$y \u2212 5 = 0\\\\Rightarrow y = 5$$<br>\r\nIt will be parallel to the x-axis.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"perpendicular to the x-axis\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Slope (m) = 0 and fixed point = (\u2212 1, 5)<br>\r\nEquation of a line is: y - 5 = 0(x \u2212 ( \u2212 1))<br>\r\n$$y \u2212 5 = 0\\\\Rightarrow y = 5$$<br>\r\nIt will be parallel to the x-axis.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"parallel to the x-axis\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Slope (m) = 0 and fixed point = (\u2212 1, 5)<br>\r\nEquation of a line is: y - 5 = 0(x \u2212 ( \u2212 1))<br>\r\n$$y \u2212 5 = 0\\\\Rightarrow y = 5$$<br>\r\nIt will be parallel to the x-axis.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Slope (m) = 0 and fixed point = (\u2212 1, 5)<br>\r\nEquation of a line is: y - 5 = 0(x \u2212 ( \u2212 1))<br>\r\n$$y \u2212 5 = 0\\\\Rightarrow y = 5$$<br>\r\nIt will be parallel to the x-axis.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The equation of the line passing through the origin and with slope 0 is\",\n                    \"text\": \"The equation of the line passing through the origin and with slope 0 is\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Point = O = (0, 0) and slope = m = 0<br>\r\nPoint Slope Form: $$(y \u2212 y_{1})= m(x \u2212 x_{1})$$<br>\r\nEquation of line: (y \u2212 0) = 0(x \u2212 0)<br>\r\nEquation of line: y = 0<br>\r\nIt is the x-axis.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"x = 0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Point = O = (0, 0) and slope = m = 0<br>\r\nPoint Slope Form: $$(y \u2212 y_{1})= m(x \u2212 x_{1})$$<br>\r\nEquation of line: (y \u2212 0) = 0(x \u2212 0)<br>\r\nEquation of line: y = 0<br>\r\nIt is the x-axis.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"y = 1\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Point = O = (0, 0) and slope = m = 0<br>\r\nPoint Slope Form: $$(y \u2212 y_{1})= m(x \u2212 x_{1})$$<br>\r\nEquation of line: (y \u2212 0) = 0(x \u2212 0)<br>\r\nEquation of line: y = 0<br>\r\nIt is the x-axis.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"x + y = \u2212 3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Point = O = (0, 0) and slope = m = 0<br>\r\nPoint Slope Form: $$(y \u2212 y_{1})= m(x \u2212 x_{1})$$<br>\r\nEquation of line: (y \u2212 0) = 0(x \u2212 0)<br>\r\nEquation of line: y = 0<br>\r\nIt is the x-axis.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"y = 0\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Point = O = (0, 0) and slope = m = 0<br>\r\nPoint Slope Form: $$(y \u2212 y_{1})= m(x \u2212 x_{1})$$<br>\r\nEquation of line: (y \u2212 0) = 0(x \u2212 0)<br>\r\nEquation of line: y = 0<br>\r\nIt is the x-axis.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Point = O = (0, 0) and slope = m = 0<br>\r\nPoint Slope Form: $$(y \u2212 y_{1})= m(x \u2212 x_{1})$$<br>\r\nEquation of line: (y \u2212 0) = 0(x \u2212 0)<br>\r\nEquation of line: y = 0<br>\r\nIt is the x-axis.\"\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 (3, 0) and (0, 3)?\",\n                    \"text\": \"What is the equation of a straight line passing through the points (3, 0) and (0, 3)?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The equation of the line will be:<br>\r\n$$(y \u2212 0) = \\\\frac{(3 \u2212 0)}{(0 \u2212 3)} (x \u2212 3)$$<br>\r\n$$y = \\\\frac{3}{\u22123}(x \u2212 3)$$<br>\r\ny = \u22121(x \u2212 3)<br>\r\ny = \u2212x + 3<br>\r\nx + y = 3\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"x \u2212 y = 3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The equation of the line will be:<br>\r\n$$(y \u2212 0) = \\\\frac{(3 \u2212 0)}{(0 \u2212 3)} (x \u2212 3)$$<br>\r\n$$y = \\\\frac{3}{\u22123}(x \u2212 3)$$<br>\r\ny = \u22121(x \u2212 3)<br>\r\ny = \u2212x + 3<br>\r\nx + y = 3\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"x + y = \u22123\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The equation of the line will be:<br>\r\n$$(y \u2212 0) = \\\\frac{(3 \u2212 0)}{(0 \u2212 3)} (x \u2212 3)$$<br>\r\n$$y = \\\\frac{3}{\u22123}(x \u2212 3)$$<br>\r\ny = \u22121(x \u2212 3)<br>\r\ny = \u2212x + 3<br>\r\nx + y = 3\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"x \u2212 y = 3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The equation of the line will be:<br>\r\n$$(y \u2212 0) = \\\\frac{(3 \u2212 0)}{(0 \u2212 3)} (x \u2212 3)$$<br>\r\n$$y = \\\\frac{3}{\u22123}(x \u2212 3)$$<br>\r\ny = \u22121(x \u2212 3)<br>\r\ny = \u2212x + 3<br>\r\nx + y = 3\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"x + y = 3\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The equation of the line will be:<br>\r\n$$(y \u2212 0) = \\\\frac{(3 \u2212 0)}{(0 \u2212 3)} (x \u2212 3)$$<br>\r\n$$y = \\\\frac{3}{\u22123}(x \u2212 3)$$<br>\r\ny = \u22121(x \u2212 3)<br>\r\ny = \u2212x + 3<br>\r\nx + y = 3\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The equation of the line will be:<br>\r\n$$(y \u2212 0) = \\\\frac{(3 \u2212 0)}{(0 \u2212 3)} (x \u2212 3)$$<br>\r\n$$y = \\\\frac{3}{\u22123}(x \u2212 3)$$<br>\r\ny = \u22121(x \u2212 3)<br>\r\ny = \u2212x + 3<br>\r\nx + y = 3\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-frequently-asked-questions-about-point-slope-form\">Frequently Asked Questions about Point Slope Form<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-3c164fdd-b52e-4e87-a774-e066345e2cd6\" 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-0-3c164fdd-b52e-4e87-a774-e066345e2cd6\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3c164fdd-b52e-4e87-a774-e066345e2cd6\"><strong>What is the difference between Point Slope Form and Slope Intercept 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-0-3c164fdd-b52e-4e87-a774-e066345e2cd6\">\n\n<ul class=\"wp-block-list\">\n<li>The Point Slope Form for finding the equation of line is given by:(y &#8211; y<sub>1<\/sub>) = m((x &#8211; x<sub>1<\/sub>), where (x, y) is just a random point on the line; (x<sub>1<\/sub>, y<sub>1<\/sub>) is a fixed point given on the line and m is the slope of the line.&nbsp;<\/li>\n\n\n\n<li>The slope intercept form equation for a straight line with a slope \u201cm\u201d and THE y &#8211; intercept as &#8220;b&#8221; is given as y = mx + b.<\/li>\n<\/ul>\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-1-3c164fdd-b52e-4e87-a774-e066345e2cd6\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3c164fdd-b52e-4e87-a774-e066345e2cd6\"><strong>What are the applications of 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-1-3c164fdd-b52e-4e87-a774-e066345e2cd6\">\n\n<p>We use the Point Slope Form for<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>finding the equation of a line with the given slope and a fixed point,<\/li>\n\n\n\n<li>plotting a graph of a line,&nbsp;<\/li>\n\n\n\n<li>deriving the two-point form.<\/li>\n<\/ul>\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-2-3c164fdd-b52e-4e87-a774-e066345e2cd6\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3c164fdd-b52e-4e87-a774-e066345e2cd6\"><strong>How is Point Slope Form different from Intercept 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-2-3c164fdd-b52e-4e87-a774-e066345e2cd6\">\n\n<ul class=\"wp-block-list\">\n<li>The Point Slope Form for finding the equation of line is given by (y &#8211; y<sub>1<\/sub>) = m ((x &#8211; x<sub>1<\/sub>) where, (x, y) is just a random point on the line; (x<sub>1<\/sub>, y<sub>1<\/sub>) is a fixed point given on the line and m is the slope of the line.&nbsp;<\/li>\n\n\n\n<li>The equation of a line in intercept form is given by: $\\frac{x}{a} + \\frac{y}{b} = 1$, where (a, 0) is the x-intercept and (0, b) is the y-intercept.<\/li>\n<\/ul>\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-3-3c164fdd-b52e-4e87-a774-e066345e2cd6\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3c164fdd-b52e-4e87-a774-e066345e2cd6\"><strong>What is the point slope formula for finding the equation of line passing through the origin?<\/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-3-3c164fdd-b52e-4e87-a774-e066345e2cd6\">\n\n<p>The equation of a line with slope m and passing through (0, 0) using the point-slope formula is y = mx.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is Point Slope Form? The point slope form of the equation of a line refers to the equation of a line with slope m and passing through the point with coordinates (x1, y1). It can be given as (y \u2212 y1) = m(x \u2212 x1) We can write the equation of a line using &#8230; <a title=\"Point Slope Form: Definition, Derivation, Facts, Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/point-slope-form\" aria-label=\"More on Point Slope Form: Definition, Derivation, Facts, Examples, FAQs\">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-36071","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\/36071","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=36071"}],"version-history":[{"count":11,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/36071\/revisions"}],"predecessor-version":[{"id":36091,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/36071\/revisions\/36091"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=36071"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=36071"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=36071"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}