Which is the graph of the linear inequality 2x – 3y < 12?<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To graph the linear inequality (2x – 3y < 12), we first rewrite it in slope-intercept form, which is useful for graphing. Here\u2019s how to do it step-by-step:<\/p>\n\n\n\n Start with the inequality: The corresponding equation for the boundary line is: Plot these two points on a coordinate plane and draw a dashed line through them. The dashed line indicates that points on the line itself are not included in the solution (since the inequality is strict: (<)).<\/p>\n\n\n\n Since the inequality is (y > \\frac{2}{3}x – 4), you will shade the region above the line. This region represents all the points where the (y)-values are greater than those on the line.<\/p>\n\n\n\n The graph of the inequality (2x – 3y < 12) consists of a dashed line with slope (\\frac{2}{3}) that passes through the points (0, -4) and (6, 0). The solution set is all the points above this line, indicating the values of (x) and (y) that satisfy the inequality.<\/p>\n","protected":false},"excerpt":{"rendered":" Which is the graph of the linear inequality 2x – 3y < 12? The Correct Answer and Explanation is : To graph the linear inequality (2x – 3y < 12), we first rewrite it in slope-intercept form, which is useful for graphing. Here\u2019s how to do it step-by-step: Step 1: Rewrite the Inequality Start with […]<\/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-146834","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146834","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=146834"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146834\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=146834"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=146834"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=146834"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Rewrite the Inequality<\/h3>\n\n\n\n
[
2x – 3y < 12 ] To isolate (y), we can subtract (2x) from both sides: [ -3y < -2x + 12 ] Next, divide every term by (-3). Remember, when we divide by a negative number, we must reverse the inequality sign: [ y > \\frac{2}{3}x – 4
]<\/p>\n\n\n\nStep 2: Graph the Boundary Line<\/h3>\n\n\n\n
[
y = \\frac{2}{3}x – 4
]
To graph this line, we can identify two points.<\/p>\n\n\n\n\n
[
y = -4 \\quad \\Rightarrow \\quad (0, -4)
]<\/li>\n\n\n\n
[
0 = \\frac{2}{3}x – 4 \\quad \\Rightarrow \\quad \\frac{2}{3}x = 4 \\quad \\Rightarrow \\quad x = 6 \\quad \\Rightarrow \\quad (6, 0)
]<\/li>\n<\/ol>\n\n\n\nStep 3: Shade the Correct Region<\/h3>\n\n\n\n
Conclusion<\/h3>\n\n\n\n