{"id":268189,"date":"2025-07-24T01:35:52","date_gmt":"2025-07-24T01:35:52","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=268189"},"modified":"2025-07-24T01:35:55","modified_gmt":"2025-07-24T01:35:55","slug":"which-of-the-graphs-below-represents-the-equation-3x-2y-12","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/24\/which-of-the-graphs-below-represents-the-equation-3x-2y-12\/","title":{"rendered":"Which of the graphs below represents the equation 3x 2y -12"},"content":{"rendered":"\n

Which of the graphs below represents the equation 3x 2y -12? Graph A Graph B Graph \u20ac Graph D<\/p>\n\n\n\n

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

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

The correct answer is Graph B<\/strong>.<\/p>\n\n\n\n

To determine which graph represents the equation 3x – 2y = -12, we can convert the equation into slope-intercept form, which is y = mx + b. In this form, ‘m’ represents the slope of the line, and ‘b’ represents the y-intercept, which is the point where the line crosses the vertical y-axis.<\/p>\n\n\n\n

First, let’s rearrange the equation 3x – 2y = -12 to solve for y:<\/p>\n\n\n\n

    \n
  1. Subtract 3x from both sides of the equation:
    -2y = -3x – 12<\/li>\n\n\n\n
  2. Divide every term by -2 to isolate y:
    y = (-3x \/ -2) – (12 \/ -2)<\/li>\n\n\n\n
  3. Simplify the expression:
    y = (3\/2)x + 6<\/li>\n<\/ol>\n\n\n\n

    From this slope-intercept form, we can identify two key features of the graph. The y-intercept (b) is 6. This means the line must pass through the point (0, 6) on the y-axis. The slope (m) is 3\/2. A positive slope indicates that the line will rise as it moves from left to right. Specifically, a slope of 3\/2 means that for every 3 units the line goes up (the rise), it will move 2 units to the right (the run).<\/p>\n\n\n\n

    Now, let’s examine the four graphs:<\/p>\n\n\n\n

      \n
    • Graph A<\/strong>\u00a0has a y-intercept of 6, but its slope is negative (it goes down from left to right). This is incorrect.<\/li>\n\n\n\n
    • Graph C<\/strong>\u00a0and\u00a0Graph D<\/strong>\u00a0do not match the required slope of 3\/2. Graph D has a negative slope, and Graph C has a positive slope that is less steep than 3\/2.<\/li>\n\n\n\n
    • Graph B<\/strong>\u00a0has a y-intercept at (0, 6). To check the slope, we can start at the y-intercept (0, 6) and move 3 units up and 2 units to the right, which would lead to the point (2, 9). Alternatively, we can see that the line also passes through the point (-4, 0). Moving from (-4, 0) to (0, 6), the rise is 6 and the run is 4. The slope is rise\/run = 6\/4, which simplifies to 3\/2.<\/li>\n<\/ul>\n\n\n\n

      Therefore, Graph B is the only graph with a y-intercept of 6 and a slope of 3\/2, correctly representing the equation y = (3\/2)x + 6.<\/p>\n\n\n\n

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

      Which of the graphs below represents the equation 3x 2y -12? Graph A Graph B Graph \u20ac Graph D The Correct Answer and Explanation is: The correct answer is Graph B. To determine which graph represents the equation 3x – 2y = -12, we can convert the equation into slope-intercept form, which is y = mx […]<\/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-268189","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/268189","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=268189"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/268189\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=268189"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=268189"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=268189"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}