{"id":228966,"date":"2025-06-07T19:01:02","date_gmt":"2025-06-07T19:01:02","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=228966"},"modified":"2025-06-07T19:01:04","modified_gmt":"2025-06-07T19:01:04","slug":"practice-applying-the-slope-intercept-form-of-an-equation","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/07\/practice-applying-the-slope-intercept-form-of-an-equation\/","title":{"rendered":"Practice applying the slope-intercept form of an equation."},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Practice applying the slope-intercept form of an equation. Which graph represents the function<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">y=32\u200bx\u22122<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This equation is in <strong>slope-intercept form<\/strong>:y=mx+by = mx + by=mx+b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>m=23m = \\frac{2}{3}m=32\u200b is the <strong>slope<\/strong><\/li>\n\n\n\n<li>b=\u22122b = -2b=\u22122 is the <strong>y-intercept<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Identify the y-intercept<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The y-intercept tells us where the line crosses the <strong>y-axis<\/strong>. For this equation, the line should cross the y-axis at (0,\u22122)(0, -2)(0,\u22122). This is our starting point on the graph.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Use the slope<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The slope 23\\frac{2}{3}32\u200b means &#8220;rise over run&#8221; \u2014 for every 3 units you move to the right (positive x-direction), you go up 2 units (positive y-direction).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, starting from (0,\u22122)(0, -2)(0,\u22122), you should move:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Right 3 units<\/li>\n\n\n\n<li>Up 2 units<br>This should give you the next point at (3,0)(3, 0)(3,0)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Analyze the graphs<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Let&#8217;s match this to the correct graph:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>third graph from the left<\/strong>:\n<ul class=\"wp-block-list\">\n<li>It has a <strong>y-intercept at -2<\/strong><\/li>\n\n\n\n<li>From (0,\u22122)(0, -2)(0,\u22122), moving right 3 and up 2 reaches (3,0)(3, 0)(3,0)<\/li>\n\n\n\n<li>This matches the slope of 23\\frac{2}{3}32\u200b<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 <strong>Therefore, the third graph from the left is the correct answer.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation Summary<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">To determine which graph represents the equation y=23x\u22122y = \\frac{2}{3}x &#8211; 2y=32\u200bx\u22122, we begin by recognizing that this is written in <strong>slope-intercept form<\/strong>, y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept. In this equation, the slope mmm is 23\\frac{2}{3}32\u200b, and the y-intercept bbb is -2.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This means the graph should cross the y-axis at (0,\u22122)(0, -2)(0,\u22122), which is the starting point of the line. From there, we use the slope 23\\frac{2}{3}32\u200b, which tells us how to move from one point to the next. A slope of 23\\frac{2}{3}32\u200b means that for every 3 units we move to the right on the x-axis, we move up 2 units on the y-axis. From (0,\u22122)(0, -2)(0,\u22122), moving right 3 units and up 2 units leads us to the point (3,0)(3, 0)(3,0), confirming the direction and steepness of the line.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Looking closely at the graphs, the third graph from the left matches both the y-intercept at -2 and the positive slope of 23\\frac{2}{3}32\u200b. None of the other graphs align with both the correct slope and y-intercept. Therefore, this is the only correct representation of the equation.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Understanding how to interpret slope and y-intercept on a graph is crucial in algebra. It allows us to visually analyze relationships between variables and determine accurate graphical representations of linear equations.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner4-665.jpeg\" alt=\"\" class=\"wp-image-228967\"\/><\/figure>\n\n\n","protected":false},"excerpt":{"rendered":"<p>Practice applying the slope-intercept form of an equation. Which graph represents the function ? The Correct Answer and Explanation is: y=32\u200bx\u22122 This equation is in slope-intercept form:y=mx+by = mx + by=mx+b Where: Step 1: Identify the y-intercept The y-intercept tells us where the line crosses the y-axis. For this equation, the line should cross the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-228966","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228966","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=228966"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228966\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=228966"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=228966"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=228966"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}