{"id":224492,"date":"2025-06-03T07:05:40","date_gmt":"2025-06-03T07:05:40","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=224492"},"modified":"2025-06-03T07:05:42","modified_gmt":"2025-06-03T07:05:42","slug":"the-table-shows-the-cost-of-buying-pencils-at-the-school-bookstore-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/03\/the-table-shows-the-cost-of-buying-pencils-at-the-school-bookstore-2\/","title":{"rendered":"The table shows the cost of buying pencils at the school bookstore."},"content":{"rendered":"\n

The table shows the cost of buying pencils at the school bookstore. If the data were graphed as
, where
is the number of pencils and
is the cost, what would
, the slope of the line, represent? Cost of Pencils Number of Pencils Cost 3
2.45 12
6.30 the number of pencils that can be purchased for
3 the cost of purchasing three pencils the cost of purchasing one pencil Done?<\/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: The cost of purchasing one pencil<\/strong><\/p>\n\n\n\n

\n\n\n\n

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

The question is asking about the meaning of the slope<\/strong> (m) in the linear equation c=mp+bc = mp + b, where:<\/p>\n\n\n\n

    \n
  • pp is the number of pencils,<\/li>\n\n\n\n
  • cc is the total cost,<\/li>\n\n\n\n
  • mm is the slope, and<\/li>\n\n\n\n
  • bb is the y-intercept.<\/li>\n<\/ul>\n\n\n\n

    In this context, the slope mm represents the rate of change<\/strong> of cost with respect to the number of pencils \u2014 essentially, how much the cost increases for each additional pencil purchased<\/strong>.<\/p>\n\n\n\n

    To determine this, we calculate the slope using two data points from the table. Let’s use:<\/p>\n\n\n\n

      \n
    • (3 pencils, $1.05)<\/li>\n\n\n\n
    • (7 pencils, $2.45)<\/li>\n<\/ul>\n\n\n\n

      Using the slope formula: m=\u0394c\u0394p=2.45\u22121.057\u22123=1.404=0.35m = \\frac{\\Delta c}{\\Delta p} = \\frac{2.45 – 1.05}{7 – 3} = \\frac{1.40}{4} = 0.35<\/p>\n\n\n\n

      So, the slope m=0.35m = 0.35, which means each pencil costs $0.35<\/strong>. The units of the slope are dollars per pencil<\/strong>.<\/p>\n\n\n\n

      Now, let\u2019s analyze what that slope represents among the answer choices:<\/p>\n\n\n\n

        \n
      • “The number of pencils that can be purchased for $1” \u2192 That would be the reciprocal (about 2.86), not the slope.<\/li>\n\n\n\n
      • “The number of pencils that can be purchased for $3” \u2192 Also a reciprocal-based value, not the slope.<\/li>\n\n\n\n
      • “The cost of purchasing three pencils” \u2192 That would be 3 \u00d7 0.35 = $1.05, which is a specific total, not the rate.<\/li>\n\n\n\n
      • \u2705 “The cost of purchasing one pencil”<\/strong> \u2192 This matches exactly with the definition and calculation of slope: $0.35 per pencil<\/strong>.<\/li>\n<\/ul>\n\n\n\n

        Thus, the slope mm represents the cost of purchasing one pencil<\/strong>, making that the correct and most logical answer.<\/p>\n\n\n\n

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

        The table shows the cost of buying pencils at the school bookstore. If the data were graphed as, whereis the number of pencils andis the cost, what would, the slope of the line, represent? Cost of Pencils Number of Pencils Cost 32.45 126.30 the number of pencils that can be purchased for3 the cost of […]<\/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-224492","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224492","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=224492"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224492\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=224492"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=224492"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=224492"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}