{"id":225203,"date":"2025-06-04T05:08:50","date_gmt":"2025-06-04T05:08:50","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=225203"},"modified":"2025-06-04T05:08:52","modified_gmt":"2025-06-04T05:08:52","slug":"which-equation-represents-the-graphed-function-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/04\/which-equation-represents-the-graphed-function-3\/","title":{"rendered":"Which equation represents the graphed function"},"content":{"rendered":"\n

Which equation represents the graphed function? y = -3x + 3 y = 3x – 3 y = 3x – \\frac{1}{3} y = -\\frac{1}{3}x + 3<\/p>\n\n\n\n

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

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

To find which equation represents the graphed function, we need to identify two key features from the graph:<\/p>\n\n\n\n

1. Y-Intercept<\/strong><\/h3>\n\n\n\n

From the graph, the line passes through the point (0,3)(0, 3). This is the y-intercept<\/strong>, which tells us the value of yy when x=0x = 0.
So, the equation must be of the form: y=mx+3y = mx + 3<\/p>\n\n\n\n

This eliminates any options without “+ 3” at the end. We are now left with:<\/p>\n\n\n\n

    \n
  • y=\u22123x+3y = -3x + 3<\/li>\n\n\n\n
  • y=\u221213x+3y = -\\frac{1}{3}x + 3<\/li>\n<\/ul>\n\n\n\n

    2. Slope (m)<\/strong><\/h3>\n\n\n\n

    The line also passes through the point (3,2)(3, 2).
    We can calculate the slope mm using the slope formula: m=y2\u2212y1x2\u2212x1=2\u221233\u22120=\u221213m = \\frac{y_2 – y_1}{x_2 – x_1} = \\frac{2 – 3}{3 – 0} = \\frac{-1}{3}<\/p>\n\n\n\n

    So, the slope is \u221213-\\frac{1}{3}.<\/p>\n\n\n\n

    Now plug that slope into the equation with the correct y-intercept: y=\u221213x+3y = -\\frac{1}{3}x + 3<\/p>\n\n\n\n

    Thus, the correct answer is:<\/p>\n\n\n\n

    D) y=\u221213x+3y = -\\frac{1}{3}x + 3<\/strong><\/p>\n\n\n\n

    \n\n\n\n

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

    The graph represents a linear function, and the equation of a line is generally written in slope-intercept form<\/strong>: y=mx+by = mx + b<\/p>\n\n\n\n

    Where:<\/p>\n\n\n\n

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

      From the graph, we can see that the line crosses the y-axis at y=3y = 3, so b=3b = 3. That means any correct equation must end with +3<\/strong>. This already eliminates two of the answer choices.<\/p>\n\n\n\n

      Next, to find the slope, we identify two points the line passes through: (0,3)(0, 3) and (3,2)(3, 2).
      Using the slope formula: m=change in ychange in x=2\u221233\u22120=\u221213m = \\frac{\\text{change in } y}{\\text{change in } x} = \\frac{2 – 3}{3 – 0} = \\frac{-1}{3}<\/p>\n\n\n\n

      The slope is negative, meaning the line is decreasing, which matches the graph.<\/p>\n\n\n\n

      So the correct equation becomes: y=\u221213x+3y = -\\frac{1}{3}x + 3<\/p>\n\n\n\n

      This matches answer choice D<\/strong>, making it the correct representation of the graphed function.<\/p>\n\n\n\n

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

      Which equation represents the graphed function? y = -3x + 3 y = 3x – 3 y = 3x – \\frac{1}{3} y = -\\frac{1}{3}x + 3 The Correct Answer and Explanation is: To find which equation represents the graphed function, we need to identify two key features from the graph: 1. Y-Intercept From the graph, […]<\/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-225203","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225203","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=225203"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225203\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=225203"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=225203"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=225203"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}