{"id":29229,"date":"2023-05-11T08:27:38","date_gmt":"2023-05-11T08:27:38","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=29229"},"modified":"2024-03-15T06:29:27","modified_gmt":"2024-03-15T06:29:27","slug":"y-mx-b-definition-slope-intercept-form-examples-facts","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/y-mx-b","title":{"rendered":"y = mx + b :\u2013 Definition, Slope Intercept Form, Examples, Facts"},"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-b95f891b-b1d6-40fb-b63a-cf99b577fa55\" 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\/y-mx-b#0-what-is-y-mx-b>What Is y $=$ mx $+$ b?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/y-mx-b#1-how-to-find-y-mx-b>How to Find y $=$ mx $+$ b<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/y-mx-b#3-writing-an-equation-in-the-slope-intercept-form->Writing an Equation in the Slope Intercept Form<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/y-mx-b#6-solved-examples-on-y-mx-b>Solved Examples on y $=$ mx $+$ b<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/y-mx-b#7-practice-problems-on-y-mx-b>Practice Problems on y $=$ mx $+$ b<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/y-mx-b#8-frequently-asked-questions-on-y-mx-b>Frequently Asked Questions on y $=$ mx $+$ b<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-y-mx-b\">What Is y $=$ mx $+$ b?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The equation of line can be written in different forms: <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/two-point-form\">two-point form<\/a>, slope-intercept form, standard form. So, what does slope intercept form look like?<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The equation y $= mx + b$ represents the slope-intercept form of a straight line.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">It is the most simple since it is based on just two values and requires no complex calculations.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s understand the meaning of $y = mx + b$.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">x and y<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">x and y are coordinates of any two points on the line. So, x and y are variables.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">What is m?&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">m in $y = mx + b$ represents the slope of the line. It tells us how steep the line is.&nbsp;<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">What is b in $y = mx + b$?&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">It\u2019s the y-intercept of the line. It\u2019s the point at which the line intersects the y-axis.&nbsp;&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"378\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/parts-of-y-mx-b.png\" alt=\"Parts of y = mx + b\" class=\"wp-image-40975\" title=\"Parts of y = mx + b\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/parts-of-y-mx-b.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/parts-of-y-mx-b-300x183.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Note: <\/strong>Sometimes the y-intercept is also represented using the letter \u201cc\u201d and in that case, the equation of line becomes $y = mx + c$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"496\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/y-mx-c-equation-of-line.png\" alt=\"y = mx + c equation of line\" class=\"wp-image-40976\" title=\"y = mx + c equation of line\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/y-mx-c-equation-of-line.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/y-mx-c-equation-of-line-300x240.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example:<\/strong> <strong>Find the equation of a line having slope 3 and y-intercept 2.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, $m = 3$ and $b = 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Equation of line using the slope-intercept form is $y = mx + b$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Required equation of the line: $y = 3x + 2$<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/10-and-100-more-than-the-same-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_1_10_100_more_same_num_pt.png\" alt=\"10 and 100 More than the Same Number 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\">10 and 100 More than the Same Number 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-1-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\/add_sub_facts_add_make_10_pt.png\" alt=\"Add 1-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\">Add 1-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\/add-10-to-a-3-digit-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_10_number_pt.png\" alt=\"Add 10 to a 3-Digit Number 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 10 to a 3-Digit Number 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-100-to-a-3-digit-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_100_horizontal_pt.png\" alt=\"Add 100 to a 3-Digit Number 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 100 to a 3-Digit Number 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-2-digit-and-1-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\/add_sub_pv_add_2d_1d_match_pt.png\" alt=\"Add 2-Digit and 1-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\">Add 2-Digit and 1-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\/add-2-digit-numbers-by-regrouping\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_regrp_2d_2d_vertical_pt.png\" alt=\"Add 2-Digit Numbers By Regrouping 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 2-Digit Numbers By Regrouping 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-3-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_3_no_pt.png\" alt=\"Add 3 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 3 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\/add-3-numbers-in-any-order\" 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_shifty_bridges_4_gm.png\" alt=\"Add 3 Numbers in Any Order 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 3 Numbers in Any Order 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-3-numbers-using-groups-of-objects\" 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_using_model_pt.png\" alt=\"Add 3 Numbers Using Groups of Objects 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 3 Numbers Using Groups of Objects 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-3-numbers-using-model\" 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_3_no_using_models_pt.png\" alt=\"Add 3 Numbers using Model 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 3 Numbers using Model 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-how-to-find-y-mx-b\">How to Find y $=$ mx $+$ b<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s derive the slope-intercept form. Consider a line whose y-intercept is b. In simple words, the line passes through the point (0,b). Let (x,y) be the coordinates of any point on the line.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, we have coordinates of two points on the line: (x,y) and (0,b).&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let the slope of the given line be m.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The formula to find the slope of the straight line is<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m = \\frac{change\\; in\\; y}{change\\; in\\; x} = \\frac{Difference\\; in\\; y\\;-\\;coordinates}{Difference\\; in\\; x\\;-\\;coordinates}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, if the points $(x_1,\\;y_1)$ and $(x_2,\\;y_2)$ lie on the given line.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"460\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/y-mx-b.png\" alt=\"y = mx + b\" class=\"wp-image-40978\" title=\"y = mx + b\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/y-mx-b.png 621w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/y-mx-b-300x222.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We can find the slope as<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"376\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/finding-the-slope-m-in-y-mx-b.png\" alt=\"Finding the slope m in y = mx + b\" class=\"wp-image-40979\" title=\"Finding the slope m in y = mx + b\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/finding-the-slope-m-in-y-mx-b.png 621w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/finding-the-slope-m-in-y-mx-b-300x182.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, in our case<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow m = \\frac{y \\;-\\; b}{x \\;-\\; 0}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow m = \\frac{y \\;-\\; b}{x}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow mx = y\\;-\\;b$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow y = mx + b$&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"344\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/derivation-of-y-mx-b.png\" alt=\"Derivation of y = mx + b\" class=\"wp-image-40980\" title=\"Derivation of y = mx + b\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/derivation-of-y-mx-b.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/derivation-of-y-mx-b-300x166.png 300w\" 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\/10-and-100-more-than-a-3-digit-number\" 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\" 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});\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-y-mx-b-at-origin\">y $=$ mx $+$ b at Origin<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s understand how to solve $y = mx + b$ at origin. The equation of a straight line with slope \u201cm\u201d passing through the origin (0,0) is given as:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$y = \\frac{y \\;-\\; 0}{x \\;-\\; 0}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$y = mx$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, for any line passing through origin, the y-intercept is 0.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-writing-an-equation-in-the-slope-intercept-form-\"><strong>Writing an Equation in the Slope Intercept Form<\/strong><\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In this section, we will learn to write an equation in the slope intercept form.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"476\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/writing-equation-of-a-line-in-slope-intercept-form.png\" alt=\"Writing equation of a line in slope intercept form\" class=\"wp-image-40981\" title=\"Writing equation of a line in slope intercept form\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/writing-equation-of-a-line-in-slope-intercept-form.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/writing-equation-of-a-line-in-slope-intercept-form-300x230.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example: Let\u2019s write the equation of the line that passes through the points <\/strong><strong>(0,3)<\/strong><strong> and <\/strong><strong>(2,7)<\/strong><strong> in slope-intercept form.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, $x_1 = 0,\\;y_1 = 3,\\;X_2 = 2,\\; , y_2 = 7$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The slope-intercept form is $y = mx + b$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The line passes through the point (0, 3). Thus, the y- intercept of the line is 3.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, $b = 3$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The slope is calculated as&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m = \\frac{y_2 \\;-\\; y_1}{x_2 \\;-\\; x_1}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m = \\frac{7 \\;-\\; 3}{2 \\;-\\; 0}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m = \\frac{4}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m = 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Putting these values in the standard equation, we get-<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$y = 2x + 3$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-facts-about-y-mx-b\">Facts about y $=$ mx $+$ b<\/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-4fc3f8e1 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<p class=\"eplus-wrapper wp-block-paragraph\">Slopes of two parallel lines are always equal. So, we can identify two parallel lines using their equations in the slope-intercept form.<br>The product of the slopes of two mutually perpendicular lines equals to $-1$. So, we can identify two perpendicular lines using their equations in the slope-intercept form.<strong>Example: <\/strong>The lines $y = \\frac{5}{6} x + 2$&nbsp; and $y = \\frac{-6}{5} x + 2$ are perpendicular since the product of the slopes is $\\frac{5}{6} \\times \\frac{-6}{5} = \\;-\\;1$<\/p>\n<\/div><\/div>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"412\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/identify-parallel-lines-using-slope-intercept-form.png\" alt=\"Identify parallel lines using slope intercept form\" class=\"wp-image-40982\" title=\"Identify parallel lines using slope intercept form\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/identify-parallel-lines-using-slope-intercept-form.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/identify-parallel-lines-using-slope-intercept-form-300x199.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In this article, we learnt about slope intercept form $y = mx + b$, the formula to find the slope, and writing the equation of a line using slope-intercept form. Let\u2019s solve a few examples!<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-solved-examples-on-y-mx-b\">Solved Examples on y $=$ mx $+$ b<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>1.&nbsp; Find the slope of the line joining the points P<\/strong>$(0,\\; \u2013\\;1)$<strong> and Q<\/strong>$(4,\\;1)$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The two points on the line are P$(0,\\; \u20132)$ and Q$(4,\\; 1)$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that, the slope of line passing through the points $(x_1,\\;x_1)$ and $(x_2,\\; y_2)$ is given by<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m = \\frac{y_2 \\;-\\; y_1}{x_2 \\;-\\; x_1}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m = \\frac{\\;-\\;2 \\;-\\; 1}{0 \\;-\\; 4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m = \\frac{\\;-3}{-\\;4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m = \\frac{3}{4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>2. Find the equation of line passing through points P<\/strong>$(\u2013\\;2,\\; 5)$<strong> and Q<\/strong>$(0,\\; \u2013\\;3)$<strong> and having y-intercept 3.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">P$(\u2013\\;2,\\; 5)$ and Q$(0,\\; \u2013\\;3)$ are the two points on the line. Therefore, slope of the line is given by&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m = \\frac{5 \\;-\\; ( \\;-\\; 3)}{ \\;-\\; 2 \\;-\\; 0} = \\frac{8}{\\;-\\;2} = \\;-\\;4$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">y-intercept $= 3$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, the equation of line is $y = \\;-\\;4x + 3$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>3. What is the slope of the line: <\/strong>$y = \\;\u2212\\;5x + 17$<strong>?<\/strong>.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If we compare the given equation with $y = mx + b$, where m is the slope and b is the y-intercept, then we get,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A slope of the line whose equation is $y = \\;-\\;5x + 17$ is $\\;-\\;2$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m = \\;-\\;5$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>4. If the slope of a straight line is 3 and y-intercept is 4, then find the equation of the line.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that the equation of line in slope-intercept form is given by:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$y = mx + b$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Given, $m = 3$ and $b = 4$, thus, the required equation is:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$y = 3x + 4$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>5. What is the slope and y-intercept of the equation <\/strong>$y = 2x$<strong>?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If we compare the given equation with $y = mx + b$, where m is the slope and b is the y-intercept, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Slope $= m = 2$ and y-intercept $= b = 0<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-practice-problems-on-y-mx-b\">Practice Problems on y $=$ mx $+$ b<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">y $=$ mx $+$ b \u2013 Definition, Slope Intercept Form, Examples, Facts<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/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 the line $y = 2x +3$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">2<\/div><div class=\"spq_answer_block\" data-value=\"1\">3<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\;-\\;2$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\;-\\;3$<\/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: 2<br\/>Comparing the equation of the line with the slope-intercept form $y = mx + b$, we get slope $= m = 2$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What is the slope of a line joining two points $(4,\\; 8)$ and $(\\;-\\;7,\\; 1)$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{7}{10}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{7}{11}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{17}{11}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{7}{15}$<\/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: $\\frac{7}{11}$<br\/>The slope of line joining two points $(4,\\; 8)$ and $(\\;-\\;7,\\; 1)$ is calculated by<br>\r\n$m =  \\frac{1 \\;-\\; 8}{\\;-\\; 4 \\;-\\;7} = \\frac{\\;-\\;7}{\\;-\\;11} = \\frac{7}{11}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">What is the slope of the line: $3y = 2x + 9$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{1}{10}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{2}{3}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{4}{5}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{14}{11}$<\/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: $\\frac{2}{3}$<br\/>Given equation of line is $3y = 2x + 9$.<br>\r\n$y = \\frac{2}{3} x + 3$<br>\r\nComparing with $y = mx + b$, we get<br>\r\nslope $= m = \\frac{2}{3}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">What is the slope-intercept form of a line with slope 3 and y-intercept -2?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$y =  x + 2$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$y = 4x + 5$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$y = 10x + 12$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$y = 3 x \\;-\\; 2$<\/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: $y = 3 x \\;-\\; 2$<br\/>The slope-intercept form of a line is $y = mx + b$.<br>\r\nThus, the equation of line is $y = 3x -2$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">The lines $y = 2x + 1$ and $y = 2x\\;-\\;1$ are<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">parallel<\/div><div class=\"spq_answer_block\" data-value=\"1\">perpendicular<\/div><div class=\"spq_answer_block\" data-value=\"2\">not parallel<\/div><div class=\"spq_answer_block\" data-value=\"3\">intersecting lines<\/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<br\/>The slopes of two parallel lines are equal. The slopes of $y = 2x + 1$ and $y = 2x\\;-\\;1$ is 2. So, they are parallel.<\/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\": \"y $$=$$ mx $$+$$ b \u2013 Definition, Slope Intercept Form, Examples, Facts\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"y $$=$$ mx $$+$$ b \u2013 Definition\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the slope of the line $$y = 2x +3$$?\",\n                    \"text\": \"What is the slope of the line $$y = 2x +3$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Comparing the equation of the line with the slope-intercept form $$y = mx + b$$, we get slope $$= m = 2$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Comparing the equation of the line with the slope-intercept form $$y = mx + b$$, we get slope $$= m = 2$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\;-\\\\;2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Comparing the equation of the line with the slope-intercept form $$y = mx + b$$, we get slope $$= m = 2$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\;-\\\\;3$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Comparing the equation of the line with the slope-intercept form $$y = mx + b$$, we get slope $$= m = 2$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"2\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Comparing the equation of the line with the slope-intercept form $$y = mx + b$$, we get slope $$= m = 2$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Comparing the equation of the line with the slope-intercept form $$y = mx + b$$, we get slope $$= m = 2$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the slope of a line joining two points $$(4,\\\\; 8)$$ and $$(\\\\;-\\\\;7,\\\\; 1)$$?\",\n                    \"text\": \"What is the slope of a line joining two points $$(4,\\\\; 8)$$ and $$(\\\\;-\\\\;7,\\\\; 1)$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The slope of line joining two points $$(4,\\\\; 8)$$ and $$(\\\\;-\\\\;7,\\\\; 1)$$ is calculated by<br>\r\n$$m =  \\\\frac{1 \\\\;-\\\\; 8}{\\\\;-\\\\; 4 \\\\;-\\\\;7} = \\\\frac{\\\\;-\\\\;7}{\\\\;-\\\\;11} = \\\\frac{7}{11}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{7}{10}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The slope of line joining two points $$(4,\\\\; 8)$$ and $$(\\\\;-\\\\;7,\\\\; 1)$$ is calculated by<br>\r\n$$m =  \\\\frac{1 \\\\;-\\\\; 8}{\\\\;-\\\\; 4 \\\\;-\\\\;7} = \\\\frac{\\\\;-\\\\;7}{\\\\;-\\\\;11} = \\\\frac{7}{11}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{17}{11}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The slope of line joining two points $$(4,\\\\; 8)$$ and $$(\\\\;-\\\\;7,\\\\; 1)$$ is calculated by<br>\r\n$$m =  \\\\frac{1 \\\\;-\\\\; 8}{\\\\;-\\\\; 4 \\\\;-\\\\;7} = \\\\frac{\\\\;-\\\\;7}{\\\\;-\\\\;11} = \\\\frac{7}{11}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{7}{15}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The slope of line joining two points $$(4,\\\\; 8)$$ and $$(\\\\;-\\\\;7,\\\\; 1)$$ is calculated by<br>\r\n$$m =  \\\\frac{1 \\\\;-\\\\; 8}{\\\\;-\\\\; 4 \\\\;-\\\\;7} = \\\\frac{\\\\;-\\\\;7}{\\\\;-\\\\;11} = \\\\frac{7}{11}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{7}{11}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The slope of line joining two points $$(4,\\\\; 8)$$ and $$(\\\\;-\\\\;7,\\\\; 1)$$ is calculated by<br>\r\n$$m =  \\\\frac{1 \\\\;-\\\\; 8}{\\\\;-\\\\; 4 \\\\;-\\\\;7} = \\\\frac{\\\\;-\\\\;7}{\\\\;-\\\\;11} = \\\\frac{7}{11}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The slope of line joining two points $$(4,\\\\; 8)$$ and $$(\\\\;-\\\\;7,\\\\; 1)$$ is calculated by<br>\r\n$$m =  \\\\frac{1 \\\\;-\\\\; 8}{\\\\;-\\\\; 4 \\\\;-\\\\;7} = \\\\frac{\\\\;-\\\\;7}{\\\\;-\\\\;11} = \\\\frac{7}{11}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the slope of the line: $$3y = 2x + 9$$?\",\n                    \"text\": \"What is the slope of the line: $$3y = 2x + 9$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Given equation of line is $$3y = 2x + 9$$.<br>\r\n$$y = \\\\frac{2}{3} x + 3$$<br>\r\nComparing with $$y = mx + b$$, we get<br>\r\nslope $$= m = \\\\frac{2}{3}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{10}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Given equation of line is $$3y = 2x + 9$$.<br>\r\n$$y = \\\\frac{2}{3} x + 3$$<br>\r\nComparing with $$y = mx + b$$, we get<br>\r\nslope $$= m = \\\\frac{2}{3}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{4}{5}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Given equation of line is $$3y = 2x + 9$$.<br>\r\n$$y = \\\\frac{2}{3} x + 3$$<br>\r\nComparing with $$y = mx + b$$, we get<br>\r\nslope $$= m = \\\\frac{2}{3}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{14}{11}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Given equation of line is $$3y = 2x + 9$$.<br>\r\n$$y = \\\\frac{2}{3} x + 3$$<br>\r\nComparing with $$y = mx + b$$, we get<br>\r\nslope $$= m = \\\\frac{2}{3}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{2}{3}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Given equation of line is $$3y = 2x + 9$$.<br>\r\n$$y = \\\\frac{2}{3} x + 3$$<br>\r\nComparing with $$y = mx + b$$, we get<br>\r\nslope $$= m = \\\\frac{2}{3}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Given equation of line is $$3y = 2x + 9$$.<br>\r\n$$y = \\\\frac{2}{3} x + 3$$<br>\r\nComparing with $$y = mx + b$$, we get<br>\r\nslope $$= m = \\\\frac{2}{3}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the slope-intercept form of a line with slope 3 and y-intercept -2?\",\n                    \"text\": \"What is the slope-intercept form of a line with slope 3 and y-intercept -2?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The slope-intercept form of a line is $$y = mx + b$$.<br>\r\nThus, the equation of line is $$y = 3x -2$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$y =  x + 2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The slope-intercept form of a line is $$y = mx + b$$.<br>\r\nThus, the equation of line is $$y = 3x -2$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$y = 4x + 5$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The slope-intercept form of a line is $$y = mx + b$$.<br>\r\nThus, the equation of line is $$y = 3x -2$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$y = 10x + 12$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The slope-intercept form of a line is $$y = mx + b$$.<br>\r\nThus, the equation of line is $$y = 3x -2$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$y = 3 x \\\\;-\\\\; 2$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The slope-intercept form of a line is $$y = mx + b$$.<br>\r\nThus, the equation of line is $$y = 3x -2$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The slope-intercept form of a line is $$y = mx + b$$.<br>\r\nThus, the equation of line is $$y = 3x -2$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The lines $$y = 2x + 1$$ and $$y = 2x\\\\;-\\\\;1$$ are\",\n                    \"text\": \"The lines $$y = 2x + 1$$ and $$y = 2x\\\\;-\\\\;1$$ are\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The slopes of two parallel lines are equal. The slopes of $$y = 2x + 1$$ and $$y = 2x\\\\;-\\\\;1$$ is 2. So, they are parallel.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"perpendicular\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The slopes of two parallel lines are equal. The slopes of $$y = 2x + 1$$ and $$y = 2x\\\\;-\\\\;1$$ is 2. So, they are parallel.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"not parallel\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The slopes of two parallel lines are equal. The slopes of $$y = 2x + 1$$ and $$y = 2x\\\\;-\\\\;1$$ is 2. So, they are parallel.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"intersecting lines\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The slopes of two parallel lines are equal. The slopes of $$y = 2x + 1$$ and $$y = 2x\\\\;-\\\\;1$$ is 2. So, they are parallel.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"parallel\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The slopes of two parallel lines are equal. The slopes of $$y = 2x + 1$$ and $$y = 2x\\\\;-\\\\;1$$ is 2. So, they are parallel.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The slopes of two parallel lines are equal. The slopes of $$y = 2x + 1$$ and $$y = 2x\\\\;-\\\\;1$$ is 2. So, they are parallel.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-frequently-asked-questions-on-y-mx-b\">Frequently Asked Questions on y $=$ mx $+$ b<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-27d0183e-1ef8-481d-8d0a-77e216ce8606\" 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-0-27d0183e-1ef8-481d-8d0a-77e216ce8606\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-27d0183e-1ef8-481d-8d0a-77e216ce8606\"><strong>What is the equation of x-axis and y-axis?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-27d0183e-1ef8-481d-8d0a-77e216ce8606\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Equation of x-axis is $y = 0$ and the equation of y-axis is $x = 0$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-27d0183e-1ef8-481d-8d0a-77e216ce8606\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-27d0183e-1ef8-481d-8d0a-77e216ce8606\"><strong>How to convert a standard form of straight line equation into the 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-1-27d0183e-1ef8-481d-8d0a-77e216ce8606\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The standard form of the equation of a straight line is given as:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Ax + By + C = 0$. &nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Rearranging this standard form, you can find the slope intercept of any straight line given in this form as,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$y = (\\frac{\\;-\\;A}{B})x + (\\frac{\\;-\\;C}{B})$, where, $\\frac{\\;-\\;A}{B}$ represents the slope of the line and $(\\frac{\\;-\\;C}{B})$ is the y-intercept.<\/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-2-27d0183e-1ef8-481d-8d0a-77e216ce8606\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-27d0183e-1ef8-481d-8d0a-77e216ce8606\"><strong>What is a positive or negative 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-2-27d0183e-1ef8-481d-8d0a-77e216ce8606\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A positive slope means y increases as x increases.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Visually, the line moves up as we go from left to right.&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/negative-slope\">negative slope<\/a> means y decreases as x increases&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Visually, the line moves down as we go from left to right.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"596\" height=\"289\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/05\/ymxb-Practice-Problems.png\" alt=\"Positive slope vs. negative slope\" class=\"wp-image-29268\" title=\"Positive slope vs. negative slope\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/05\/ymxb-Practice-Problems.png 596w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/05\/ymxb-Practice-Problems-300x145.png 300w\" sizes=\"auto, (max-width: 596px) 100vw, 596px\" \/><\/figure>\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-3-27d0183e-1ef8-481d-8d0a-77e216ce8606\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-27d0183e-1ef8-481d-8d0a-77e216ce8606\"><strong>What is a 0 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-3-27d0183e-1ef8-481d-8d0a-77e216ce8606\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/zero-slope\">zero slope<\/a> means that y is constant and it does not change as x changes. So, the equation of line having 0 slope is $y = c$, where c is constant. It is basically a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/horizontal\">horizontal line<\/a>.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is y $=$ mx $+$ b? The equation of line can be written in different forms: two-point form, slope-intercept form, standard form. So, what does slope intercept form look like? The equation y $= mx + b$ represents the slope-intercept form of a straight line.&nbsp; It is the most simple since it is based &#8230; <a title=\"y = mx + b :\u2013 Definition, Slope Intercept Form, Examples, Facts\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/y-mx-b\" aria-label=\"More on y = mx + b :\u2013 Definition, Slope Intercept Form, Examples, Facts\">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-29229","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\/29229","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=29229"}],"version-history":[{"count":16,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/29229\/revisions"}],"predecessor-version":[{"id":40983,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/29229\/revisions\/40983"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=29229"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=29229"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=29229"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}