{"id":232297,"date":"2025-06-11T22:41:16","date_gmt":"2025-06-11T22:41:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=232297"},"modified":"2025-06-11T22:41:18","modified_gmt":"2025-06-11T22:41:18","slug":"which-graph-represents-the-equation-y-1-2x-3-a-b-c-d","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/11\/which-graph-represents-the-equation-y-1-2x-3-a-b-c-d\/","title":{"rendered":"‘Which graph represents the equation y = -1\/2x – 3? A) B) C) D) ‘"},"content":{"rendered":"\n

‘Which graph represents the equation y = -1\/2x – 3? A) B) C) D) ‘<\/p>\n\n\n\n

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

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

Correct Answer:<\/strong> The graph provided is the correct representation of the equation y = -1\/2x – 3.<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

To determine which graph correctly represents a linear equation, we can analyze the equation’s properties in the slope-intercept form, which is y = mx + b<\/strong>.<\/p>\n\n\n\n

In this form:<\/p>\n\n\n\n

    \n
  • b<\/strong>\u00a0represents the\u00a0y-intercept<\/strong>, which is the point where the line crosses the vertical y-axis.<\/li>\n\n\n\n
  • m<\/strong>\u00a0represents the\u00a0slope<\/strong>\u00a0of the line, which describes its steepness and direction. The slope is calculated as “rise over run” (the change in y divided by the change in x).<\/li>\n<\/ul>\n\n\n\n

    Step 1: Analyze the given equation.<\/strong>
    The equation is y = -1\/2x – 3.
    By comparing this to y = mx + b, we can identify:<\/p>\n\n\n\n

      \n
    • The y-intercept\u00a0b\u00a0is\u00a0-3<\/strong>.<\/li>\n\n\n\n
    • The slope\u00a0m\u00a0is\u00a0-1\/2<\/strong>.<\/li>\n<\/ul>\n\n\n\n

      Step 2: Use the y-intercept to locate a point on the graph.<\/strong>
      The y-intercept b = -3 tells us that the line must pass through the point on the y-axis where the y-value is -3. This corresponds to the coordinate point (0, -3)<\/strong>. Looking at the provided graph, we can see that the purple line clearly intersects the y-axis at -3. This is our first confirmation that the graph is correct.<\/p>\n\n\n\n

      Step 3: Use the slope to find other points and verify the line’s direction.<\/strong>
      The slope m = -1\/2 tells us about the line’s steepness. A negative slope means the line goes downwards as we move from left to right. The value -1\/2 can be interpreted as a “rise” of -1 and a “run” of 2.<\/p>\n\n\n\n

      Starting from our y-intercept (0, -3):<\/p>\n\n\n\n

        \n
      • A “rise” of -1 means we move\u00a0down 1 unit<\/strong>\u00a0(from y=-3 to y=-4).<\/li>\n\n\n\n
      • A “run” of 2 means we move\u00a0right 2 units<\/strong>\u00a0(from x=0 to x=2).<\/li>\n<\/ul>\n\n\n\n

        This leads us to a second point on the line: (2, -4)<\/strong>. If we examine the graph, the line passes directly through this point. We can repeat this process from (2, -4) to find another point at (4, -5), which also lies on the graphed line.<\/p>\n\n\n\n

        Therefore, since the graph has a y-intercept at (0, -3) and a slope of -1\/2, it is the correct visual representation of the equation y = -1\/2x – 3.<\/p>\n\n\n\n

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

        ‘Which graph represents the equation y = -1\/2x – 3? A) B) C) D) ‘ The Correct Answer and Explanation is: Correct Answer: The graph provided is the correct representation of the equation y = -1\/2x – 3. Explanation: To determine which graph correctly represents a linear equation, we can analyze the equation’s properties in the slope-intercept […]<\/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-232297","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232297","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=232297"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232297\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=232297"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=232297"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=232297"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}