{"id":229399,"date":"2025-06-08T06:57:53","date_gmt":"2025-06-08T06:57:53","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=229399"},"modified":"2025-06-08T06:57:55","modified_gmt":"2025-06-08T06:57:55","slug":"which-linear-inequality-is-represented-by-the-graph-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/08\/which-linear-inequality-is-represented-by-the-graph-2\/","title":{"rendered":"Which linear inequality is represented by the graph"},"content":{"rendered":"\n

Which linear inequality is represented by the graph?<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

ChatGPT said:<\/h6>\n\n\n\n

The graph shows a shaded region above<\/strong> a solid straight line, which represents the solution set of a linear inequality<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

Correct Linear Inequality:<\/strong><\/h3>\n\n\n\n

y\u2265x+2y \\geq x + 2y\u2265x+2<\/p>\n\n\n\n

\n\n\n\n

Explanation<\/strong><\/h3>\n\n\n\n

To determine the correct linear inequality represented by the graph, we follow these steps:<\/p>\n\n\n\n

    \n
  1. Identify the boundary line<\/strong>:
    The graph shows a straight line that intersects the y-axis at (0, 2)<\/strong> and goes through the point (\u22122, 0)<\/strong>.
    Using these two points, we can find the slope<\/strong> of the line: slope=0\u22122\u22122\u22120=\u22122\u22122=1\\text{slope} = \\frac{0 – 2}{-2 – 0} = \\frac{-2}{-2} = 1slope=\u22122\u221200\u22122\u200b=\u22122\u22122\u200b=1 So, the equation of the line is: y=x+2y = x + 2y=x+2<\/li>\n\n\n\n
  2. Determine the type of inequality<\/strong>:
    The line is solid<\/strong>, which means points on<\/strong> the line are included in the solution. This tells us the inequality symbol is \u201c\u2265\u201d<\/strong> or \u201c\u2264\u201d<\/strong> rather than a strict inequality like \u201c>\u201d or \u201c<\u201d.<\/li>\n\n\n\n
  3. Identify the shaded region<\/strong>:
    The shaded region is above<\/strong> the line. In the coordinate plane, this means that the values of y<\/strong> are greater than the values given by the line equation. Therefore, the inequality is: y\u2265x+2y \\geq x + 2y\u2265x+2<\/li>\n\n\n\n
  4. Check a test point<\/strong>:
    To verify, we can test the point (0, 4)<\/strong>, which lies in the shaded region: 4\u22650+2\u21d24\u22652\u00a0\u2713\u00a0True4 \\geq 0 + 2 \\Rightarrow 4 \\geq 2 \\text{ \u2713 True}4\u22650+2\u21d24\u22652\u00a0\u2713\u00a0True So, the inequality holds in the shaded region.<\/li>\n<\/ol>\n\n\n\n
    \n\n\n\n

    Conclusion<\/strong>:<\/h3>\n\n\n\n

    The shaded region and boundary line correspond to the inequality:y\u2265x+2\\boxed{y \\geq x + 2}y\u2265x+2\u200b<\/p>\n\n\n\n

    This inequality includes all points on and above the line y=x+2y = x + 2y=x+2.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    Which linear inequality is represented by the graph? The Correct Answer and Explanation is: ChatGPT said: The graph shows a shaded region above a solid straight line, which represents the solution set of a linear inequality. Correct Linear Inequality: y\u2265x+2y \\geq x + 2y\u2265x+2 Explanation To determine the correct linear inequality represented by the graph, […]<\/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-229399","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/229399","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=229399"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/229399\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=229399"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=229399"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=229399"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}