{"id":259992,"date":"2025-07-19T06:58:43","date_gmt":"2025-07-19T06:58:43","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=259992"},"modified":"2025-07-19T06:58:45","modified_gmt":"2025-07-19T06:58:45","slug":"choose-the-graph-for-the-inequality","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/19\/choose-the-graph-for-the-inequality\/","title":{"rendered":"Choose the graph for the inequality"},"content":{"rendered":"\n<p>Choose the graph for the inequality: y > 2x &#8211; 1<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-558.png\" alt=\"\" class=\"wp-image-259993\"\/><\/figure>\n\n\n\n<p><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>The correct answer is&nbsp;<strong>c<\/strong>.<\/p>\n\n\n\n<p>To determine the correct graph for the inequality&nbsp;y &gt; 2x &#8211; 1, we need to analyze two key components: the boundary line and the shaded region.<\/p>\n\n\n\n<p>First, let&#8217;s consider the boundary line, which is represented by the equation&nbsp;y = 2x &#8211; 1. This equation is in the slope-intercept form&nbsp;y = mx + b, where&nbsp;m&nbsp;is the slope and&nbsp;b&nbsp;is the y-intercept.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The y-intercept (b) is -1. This means the line must cross the vertical y-axis at the point (0, -1).<\/li>\n\n\n\n<li>The slope (m) is 2, which can be written as 2\/1. This means for every 1 unit you move to the right on the graph, you must move 2 units up. Starting from the y-intercept (0, -1), moving right 1 and up 2 brings us to the point (1, 1). All four graphs show a line with this correct y-intercept and slope.<\/li>\n<\/ul>\n\n\n\n<p>Next, we analyze the inequality symbol, which is&nbsp;&gt;&nbsp;(greater than).<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Because the inequality is strictly &#8220;greater than&#8221; and not &#8220;greater than or equal to&#8221; (\u2265), the points on the line\u00a0y = 2x &#8211; 1\u00a0are not part of the solution. This is represented graphically by a\u00a0<strong>dashed or dotted line<\/strong>. This criterion immediately eliminates options\u00a0<strong>a<\/strong>\u00a0and\u00a0<strong>d<\/strong>, which both feature a solid line.<\/li>\n<\/ul>\n\n\n\n<p>Finally, we determine the correct shaded region. The inequality&nbsp;y &gt; 2x &#8211; 1&nbsp;means we are looking for all the points (x, y) where the y-value is greater than the value on the line. This corresponds to the region&nbsp;<strong>above<\/strong>&nbsp;the boundary line.<br>We can also use a test point, such as the origin (0, 0), to verify the shading. Substitute x=0 and y=0 into the inequality:<br>y &gt; 2x &#8211; 1<br>0 &gt; 2(0) &#8211; 1<br>0 &gt; -1<br>This statement is true. Therefore, the point (0, 0) must be included in the shaded solution area.<\/p>\n\n\n\n<p>Comparing the remaining options,&nbsp;<strong>b<\/strong>&nbsp;and&nbsp;<strong>c<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Graph\u00a0<strong>b<\/strong>\u00a0has the correct dashed line, but the shading is below the line, which would represent\u00a0y &lt; 2x &#8211; 1.<\/li>\n\n\n\n<li>Graph\u00a0<strong>c<\/strong>\u00a0has the correct dashed line, and the shading is above the line, which includes our test point (0, 0).<\/li>\n<\/ul>\n\n\n\n<p>Therefore, graph&nbsp;<strong>c<\/strong>&nbsp;is the only option that correctly represents the inequality&nbsp;y &gt; 2x &#8211; 1.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1030.jpeg\" alt=\"\" class=\"wp-image-259998\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Choose the graph for the inequality: y > 2x &#8211; 1 The Correct Answer and Explanation is: The correct answer is&nbsp;c. To determine the correct graph for the inequality&nbsp;y &gt; 2x &#8211; 1, we need to analyze two key components: the boundary line and the shaded region. First, let&#8217;s consider the boundary line, which is [&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-259992","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/259992","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=259992"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/259992\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=259992"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=259992"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=259992"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}