{"id":"cb_question_bank:7c2bbdfc-beb9-4c6a-b196-03ec945be190","source_id":"cb_question_bank","source_item_id":"7c2bbdfc-beb9-4c6a-b196-03ec945be190","external_id":null,"ibn":"08375-DC","question_id":"11e1ab81","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The graph above shows the distance traveled d , in feet, by a product on a conveyor belt m minutes after the product is placed on the belt. Which of the following equations correctly relates d and m ?","stimulus":"The figure presents the graph of a line in the coordinate plane. The horizontal m-axis is labeled “Time, in minutes,” and the numbers 0 through 7 are indicated. The vertical d-axis is labeled “Distance traveled, in feet,” and the numbers 0 through 7 are indicated. The line passes through the points with coordinates 1 comma 2 and 3 comma 6.","stimulus_html":"<div class=\"stimulus_reference \">\n        <div class=\"standalone_image \">\n          <img src=\"/api/assets/9a32c50ca859de565f698d4d672aa8b7698b93e2cd29df241943619ac56a8fb3\" alt=\"The figure presents the graph of a line in the coordinate plane. The horizontal m-axis is labeled “Time, in minutes,” and the numbers 0 through 7 are indicated. The vertical d-axis is labeled “Distance traveled, in feet,” and the numbers 0 through 7 are indicated. The line passes through the points with coordinates 1 comma 2 and 3 comma 6.\" width=\"148\" height=\"148\"></div>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">The graph above shows the distance traveled <span class=\"italic\">d</span>, in&nbsp;feet, by a product on a conveyor belt <span class=\"italic\">m</span>&nbsp;minutes after the product is placed on the belt. Which of the following equations correctly relates <span class=\"italic\">d</span> and <span class=\"italic\">m</span> ?</p>\n","rationale_html":"<p>Choice A is correct. The line passes through the origin. Therefore, this is a relationship of the form <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6241b5c0050d6ca03fd638463d9dd745b392589dc6efda3be0d32290191abd31\" alt=\"d equals, k m\"></span>, where <span class=\"italic\"></span><span class=\"italic\">k</span> is a constant representing the slope of the graph. To find the value of <span class=\"italic\">k</span>, choose a point <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/150f09b2f228b6b1ff6d516cbe216c4da5009716c02a417f6fd4830c80bea67a\" alt=\"with coordinates m comma d\"></span> on the graph of the line other than the origin and substitute the values of <span class=\"italic\">m</span> and <span class=\"italic\">d</span> into the equation. For example, if the point <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/51485fa5d3349b96da9cb9a0ba0f68ce64a97b24ef0f81b1aa741e2afe70eedd\" alt=\"with coordinates 2 comma 4\"></span> is chosen, then <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/63c14fecf5bce284a04deab481d6d6a8689931fef8c8fbce7697c70640cda31a\" alt=\"4 equals, k times 2\"></span>, and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6dc9e8932d0abe0c20d81be28569133c9cdfe4c5f184537c20f08d7ca50d8d7c\" alt=\"k equals 2\"></span>. Therefore, the equation of the line is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f79a56356244f5fa8bc277630b0ab87c6e90cad656677758f607c322b575e864\" alt=\"d equals, 2 m\"></span>.</p><p>Choice B is incorrect and may result from calculating the slope of the line as the change in time over the change in distance traveled instead of the change in distance traveled over the change in time. Choices C and D are incorrect because each of these equations represents a line with a <span class=\"italic\">d</span>-intercept of 2. However, the graph shows a line with a <span class=\"italic\">d</span>-intercept of 0.</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.635000+00:00","source_updated_at":"2023-08-02T20:25:59.635000+00:00","options":[{"label":"A","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f79a56356244f5fa8bc277630b0ab87c6e90cad656677758f607c322b575e864\" alt=\"d equals 2 m\"></span></span>\n","ord":0},{"label":"B","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ee36312a538d81014297a9277f8822de902f20474a2b9d0841f6497225acf86d\" alt=\"d equals, one-half m\"></span></span>\n","ord":1},{"label":"C","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ed080382ff14a487c81a9a47469d674df929127dbf507d67cce4a682692752ec\" alt=\"d equals m, plus 2\"></span></span>\n","ord":2},{"label":"D","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dfa2f673a8ff358c9abfdbbaeebb5b3b9e5edf0898a594917b3bbbb9d0d0317d\" alt=\"d equals 2 m, plus 2\"></span></span>\n","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}