{"id":280189,"date":"2025-08-04T15:50:38","date_gmt":"2025-08-04T15:50:38","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=280189"},"modified":"2025-08-04T15:50:40","modified_gmt":"2025-08-04T15:50:40","slug":"slope-y-intercept","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/04\/slope-y-intercept\/","title":{"rendered":"\u00a0Slope: y-intercept"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

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

Of course. Here are the correct answers for the graphs, followed by a detailed explanation.<\/p>\n\n\n\n

Correct Answers<\/strong><\/h3>\n\n\n\n

For Graph A:<\/strong><\/p>\n\n\n\n

    \n
  • SPEED:<\/strong>\u00a00.5<\/li>\n\n\n\n
  • Y-INTERCEPT:<\/strong>\u00a02<\/li>\n\n\n\n
  • EQUATION:<\/strong>\u00a0y = 0.5x + 2<\/li>\n<\/ul>\n\n\n\n

    For Graph B:<\/strong><\/p>\n\n\n\n

      \n
    • SPEED:<\/strong>\u00a03<\/li>\n\n\n\n
    • Y-INTERCEPT:<\/strong>\u00a09<\/li>\n\n\n\n
    • EQUATION:<\/strong>\u00a0y = -3x + 9<\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

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

      The two images show distance-time graphs, which are used to represent an object’s motion. The vertical axis (y-axis) represents the distance from a starting point, and the horizontal axis (x-axis) represents time. The information requested for each graph can be found by analyzing the properties of the straight line.<\/p>\n\n\n\n

      Analysis of Graph A:<\/strong><\/p>\n\n\n\n

      The line in Graph A is moving upward from left to right, which indicates that the object is moving away from its origin at a constant speed.<\/p>\n\n\n\n

        \n
      1. Y-Intercept:<\/strong>\u00a0The y-intercept is the point where the line crosses the vertical y-axis. This point represents the object’s initial distance at time zero (x=0). By looking at the graph, we can see the line starts at the point (0, 2). Therefore, the y-intercept is 2.<\/li>\n\n\n\n
      2. Speed:<\/strong>\u00a0In a distance-time graph, the speed of the object is represented by the slope of the line. The slope is calculated as the “rise over run,” or the change in the y-values divided by the change in the x-values. We can pick two distinct points on the line to calculate this. Let’s use the starting point (0, 2) and the ending point (10, 7).\n
          \n
        • Slope (Speed) = (y\u2082 – y\u2081) \/ (x\u2082 – x\u2081) = (7 – 2) \/ (10 – 0) = 5 \/ 10 = 0.5.<\/li>\n\n\n\n
        • The speed is 0.5 units of distance per unit of time.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
        • Equation:<\/strong>\u00a0The equation of a straight line is given by the formula y = mx + b, where ‘m’ is the slope (speed) and ‘b’ is the y-intercept. Using the values we found:\n
            \n
          • m = 0.5<\/li>\n\n\n\n
          • b = 2<\/li>\n\n\n\n
          • The equation for the line in Graph A is y = 0.5x + 2.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n

            Analysis of Graph B:<\/strong><\/p>\n\n\n\n

            The line in Graph B is moving downward from left to right, indicating the object is moving back toward its origin at a constant speed.<\/p>\n\n\n\n

              \n
            1. Y-Intercept:<\/strong>\u00a0Similar to the first graph, we find the y-intercept where the line crosses the y-axis (at x=0). The line begins at the point (0, 9), so the y-intercept is 9.<\/li>\n\n\n\n
            2. Speed:<\/strong>\u00a0We calculate the slope to find the velocity. The line passes through points (0, 9) and (3, 0).\n
                \n
              • Slope = (y\u2082 – y\u2081) \/ (x\u2082 – x\u2081) = (0 – 9) \/ (3 – 0) = -9 \/ 3 = -3.<\/li>\n\n\n\n
              • The negative sign indicates the direction of motion is toward the origin. Speed, however, is a scalar quantity that measures magnitude, not direction, so it cannot be negative. We take the absolute value of the slope. The speed is |-3| = 3.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
              • Equation:<\/strong>\u00a0We use the formula y = mx + b with the slope and y-intercept we determined.\n
                  \n
                • m = -3<\/li>\n\n\n\n
                • b = 9<\/li>\n\n\n\n
                • The equation for the line in Graph B is y = -3x + 9.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n
                  \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

                  The Correct Answer and Explanation is: Of course. Here are the correct answers for the graphs, followed by a detailed explanation. Correct Answers For Graph A: For Graph B: Explanation The two images show distance-time graphs, which are used to represent an object’s motion. The vertical axis (y-axis) represents the distance from a starting point, […]<\/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-280189","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/280189","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=280189"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/280189\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=280189"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=280189"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=280189"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}