{"id":225198,"date":"2025-06-04T05:05:27","date_gmt":"2025-06-04T05:05:27","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=225198"},"modified":"2025-06-04T05:05:30","modified_gmt":"2025-06-04T05:05:30","slug":"which-equation-represents-the-graphed-function-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/04\/which-equation-represents-the-graphed-function-2\/","title":{"rendered":"Which equation represents the graphed function"},"content":{"rendered":"\n

Which equation represents the graphed function? ?<\/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 equation that represents the graphed function is: y=32x\u22123y = \\frac{3}{2}x – 3<\/p>\n\n\n\n

This is the third option in the multiple-choice list, and it has been correctly selected in the image.<\/p>\n\n\n\n

\n\n\n\n

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

To determine which equation represents the graphed line, we need to identify two key components of a linear equation in slope-intercept form: y=mx+by = mx + b<\/p>\n\n\n\n

where:<\/p>\n\n\n\n

    \n
  • mm is the slope (the rate of change or steepness of the line),<\/li>\n\n\n\n
  • bb is the y-intercept (the point where the line crosses the y-axis).<\/li>\n<\/ul>\n\n\n\n

    From the graph, we can observe that the line crosses the y-axis at the point (0,\u22123)(0, -3). This means the y-intercept, bb, is -3<\/strong>.<\/p>\n\n\n\n

    Next, we determine the slope<\/strong>. Choose two points that the line passes through. From the graph:<\/p>\n\n\n\n

      \n
    • Point A: (0,\u22123)(0, -3)<\/li>\n\n\n\n
    • Point B: (2,0)(2, 0)<\/li>\n<\/ul>\n\n\n\n

      To calculate the slope mm, use the formula: m=y2\u2212y1x2\u2212x1m = \\frac{y_2 – y_1}{x_2 – x_1}<\/p>\n\n\n\n

      Using the two points: m=0\u2212(\u22123)2\u22120=32m = \\frac{0 – (-3)}{2 – 0} = \\frac{3}{2}<\/p>\n\n\n\n

      So the slope m=32m = \\frac{3}{2}, and the y-intercept b=\u22123b = -3.<\/p>\n\n\n\n

      Putting this into slope-intercept form: y=32x\u22123y = \\frac{3}{2}x – 3<\/p>\n\n\n\n

      Now, compare this equation with the options given:<\/p>\n\n\n\n

        \n
      • Option A: \u22123x+2=y-3x + 2 = y \u2192 wrong slope and intercept<\/li>\n\n\n\n
      • Option B: \u221223x+2=y-\\frac{2}{3}x + 2 = y \u2192 wrong slope and intercept<\/li>\n\n\n\n
      • \u2705 Option C: 32x\u22123=y\\frac{3}{2}x – 3 = y \u2192 correct<\/li>\n\n\n\n
      • Option D: 2x\u22123=y2x – 3 = y \u2192 wrong slope<\/li>\n<\/ul>\n\n\n\n

        Therefore, the correct and best match is: y=32x\u22123\\boxed{y = \\frac{3}{2}x – 3}<\/p>\n\n\n\n

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

        Which equation represents the graphed function? ? The Correct Answer and Explanation is: The correct equation that represents the graphed function is: y=32x\u22123y = \\frac{3}{2}x – 3 This is the third option in the multiple-choice list, and it has been correctly selected in the image. Explanation To determine which equation represents the graphed line, we […]<\/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-225198","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225198","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=225198"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225198\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=225198"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=225198"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=225198"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}