{"id":199178,"date":"2025-03-10T20:00:17","date_gmt":"2025-03-10T20:00:17","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=199178"},"modified":"2025-03-10T20:00:20","modified_gmt":"2025-03-10T20:00:20","slug":"which-equation-is-represented-by-the-graph-below","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/10\/which-equation-is-represented-by-the-graph-below\/","title":{"rendered":"Which equation is represented by the graph below"},"content":{"rendered":"\n<p>1) Which equation is represented by the graph below?<\/p>\n\n\n\n<p>y = 0<\/p>\n\n\n\n<p>-2y = -4x + 10<\/p>\n\n\n\n<p>2y + x = 10<\/p>\n\n\n\n<p>y + 2x = -5<\/p>\n\n\n\n<p>2y = -10x &#8211; 4<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct equation represented by the given graph is:<\/p>\n\n\n\n<p><strong>-2y = -4x + 10<\/strong>, which can be simplified to <strong>y = 2x &#8211; 5<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>To identify which equation matches a given graph, consider the slope and intercept clearly visible on the graph.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>y = 0<\/strong>:\n<ul class=\"wp-block-list\">\n<li>This is a horizontal line through the origin.<\/li>\n\n\n\n<li>The graph would have no slope and remain flat at y = 0.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>-2y = -4x + 10<\/strong><em>(simplified as y = 2x &#8211; 5)<\/em>:\n<ul class=\"wp-block-list\">\n<li>This is in slope-intercept form y=mx+by = mx + b with slope m=2m = 2 and y-intercept b=\u22125b = -5.<\/li>\n\n\n\n<li>Thus, the graph slopes upward from left to right, crossing the y-axis at (0,-5).<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>2y + x = 10<\/strong><em>(simplified as y=\u221212x+5y = -\\frac{1}{2}x + 5)<\/em>:\n<ul class=\"wp-block-list\">\n<li>This line has a negative slope (-\u00bd) and intercept at (0,5), sloping downward from left to right.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>y + 2x = -5<\/strong><em>(simplified as y = -2x &#8211; 5)<\/em>:\n<ul class=\"wp-block-list\">\n<li>Negative slope (-2), crossing y-axis at (0,-5).<\/li>\n\n\n\n<li>Slopes downward, significantly steeper than option 3.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>2y = -10x &#8211; 4<\/strong><em>(simplified as y = -5x &#8211; 2)<\/em>:\n<ul class=\"wp-block-list\">\n<li>This line has a negative slope (-5), very steep, and intersects at (0,-2).<\/li>\n\n\n\n<li>Rapidly decreases from left to right.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Matching the Graph:<\/h3>\n\n\n\n<p>The line on the given graph slopes upward from left to right (positive slope), intersecting the y-axis below the x-axis. Among the provided equations, only equation <strong>-2y = -4x + 10<\/strong> simplifies to a positive slope of m=2m = 2 and intercept b=\u22125b = -5. Hence, this matches the described line perfectly.<\/p>\n\n\n\n<p>The plotted image generated clearly illustrates these differences in slope and intercept, verifying visually that the correct choice is: -2y&nbsp;=&nbsp;-4x&nbsp;+&nbsp;10&nbsp;(y&nbsp;=&nbsp;2x&nbsp;&#8211;&nbsp;5)\\textbf{-2y = -4x + 10 (y = 2x &#8211; 5)}<\/p>\n","protected":false},"excerpt":{"rendered":"<p>1) Which equation is represented by the graph below? y = 0 -2y = -4x + 10 2y + x = 10 y + 2x = -5 2y = -10x &#8211; 4 The correct answer and explanation is: The correct equation represented by the given graph is: -2y = -4x + 10, which can be [&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-199178","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199178","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=199178"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199178\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=199178"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=199178"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=199178"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}