{"id":236333,"date":"2025-06-16T07:39:24","date_gmt":"2025-06-16T07:39:24","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=236333"},"modified":"2025-06-16T07:39:25","modified_gmt":"2025-06-16T07:39:25","slug":"graph-the-inequality-y-%e2%89%a5-2x-6","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/16\/graph-the-inequality-y-%e2%89%a5-2x-6\/","title":{"rendered":"Graph the inequality y \u2265 -2x &#8211; 6"},"content":{"rendered":"\n<p>Graph the inequality y \u2265 -2x &#8211; 6<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To graph the inequality <strong>y \u2265 -2x &#8211; 6<\/strong>, begin by considering the related equation <strong>y = -2x &#8211; 6<\/strong>, which represents a straight line in slope-intercept form, where the slope is <strong>-2<\/strong> and the y-intercept is <strong>-6<\/strong>.<\/p>\n\n\n\n<p>Plot the line by first locating the y-intercept at the point <strong>(0, -6)<\/strong> on the coordinate plane. From that point, use the slope of <strong>-2<\/strong>, which indicates a downward direction: for every 1 unit increase in x, y decreases by 2 units. Move right 1 unit and down 2 units to find a second point. Connect the points to form a <strong>solid<\/strong> line because the inequality includes &#8220;equal to&#8221; (\u2265), which means the points on the line are part of the solution set.<\/p>\n\n\n\n<p>Next, determine which side of the line to shade. Since the inequality is <strong>y \u2265 -2x &#8211; 6<\/strong>, the region above the line should be shaded. This region includes all the points for which the y-values are greater than or equal to the corresponding values on the line. A simple method to verify this involves testing a point not on the line, such as <strong>(0, 0)<\/strong>. Substituting into the inequality gives:<\/p>\n\n\n\n<p><strong>0 \u2265 -2(0) &#8211; 6<\/strong><br><strong>0 \u2265 -6<\/strong> \u2014 which is true.<\/p>\n\n\n\n<p>Since the point (0, 0) satisfies the inequality, the region containing this point should be shaded.<\/p>\n\n\n\n<p>The final graph consists of a <strong>solid diagonal line<\/strong> descending from left to right, intersecting the y-axis at -6, and shading the <strong>region above<\/strong> this line, representing all coordinate pairs (x, y) that satisfy the inequality. This shaded area indicates the set of solutions to the inequality <strong>y \u2265 -2x &#8211; 6<\/strong>.<\/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-banner10-171.jpeg\" alt=\"\" class=\"wp-image-236335\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Graph the inequality y \u2265 -2x &#8211; 6 The Correct Answer and Explanation is: To graph the inequality y \u2265 -2x &#8211; 6, begin by considering the related equation y = -2x &#8211; 6, which represents a straight line in slope-intercept form, where the slope is -2 and the y-intercept is -6. Plot the line [&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-236333","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236333","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=236333"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236333\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=236333"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=236333"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=236333"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}