{"id":"cb_question_bank:5396cb18-1a0d-4138-9146-281334b3f86a","source_id":"cb_question_bank","source_item_id":"5396cb18-1a0d-4138-9146-281334b3f86a","external_id":null,"ibn":"019531-DC","question_id":"1e1027a7","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.D.","skill":"Two-variable data: Models and scatterplots","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The scatterplot above shows a company’s ice cream sales d , in dollars, and the high temperature t , in degrees Celsius (°C), on 12 different days. A line of best fit for the data is also shown. Which of the following could be an equation of the line of best fit?","stimulus":"The figure presents a scatterplot titled “Ice Cream Sales.” The horizontal axis is labeled “Temperature, in degrees Celsius,” and the integers 10 through 26, in increments of 2, are indicated. The vertical axis is labeled “Sales, in dollars,” and the integers 300 through 1,000, in increments of 100, are indicated. There are 12 data points in the scatterplot, and the line of best fit is drawn. The line of best fit begins slightly above the horizontal axis, and slightly to the right of the vertical axis, and slants upward and to the right. It passes through the point 12 comma 480 and the point 24 comma 880.","stimulus_html":"<div class=\"stimulus_reference \">\n\t<div class=\"standalone_image \"><img src=\"/api/assets/168c278f0bebde73cbd2274daa0f6dd908a2436623f04240bc7e069b78c34fba\" alt=\"The figure presents a scatterplot titled “Ice Cream Sales.” The horizontal axis is labeled “Temperature, in degrees Celsius,” and the integers 10 through 26, in increments of 2, are indicated. The vertical axis is labeled “Sales, in dollars,” and the integers 300 through 1,000, in increments of 100, are indicated. There are 12 data points in the scatterplot, and the line of best fit is drawn. The line of best fit begins slightly above the horizontal axis, and slightly to the right of the vertical axis, and slants upward and to the right. It passes through the point 12 comma 480 and the point 24 comma 880.\" width=\"208\" height=\"137\"></div>\n</div>\n","stem_html":"<p class=\"stem_paragraph \">The scatterplot above shows a company’s ice cream sales <span class=\"italic\">d</span>, in dollars, and the high temperature <span class=\"italic\">t</span>, in degrees Celsius (°C), on 12 different days. A line of best fit for the data is also shown. Which of the following could be an equation of the line of best fit?</p>\n","rationale_html":"<p>Choice D is correct. On the line of best fit, <span class=\"italic\">d</span> increases from approximately 480 to 880 between <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/191b9de50249c5cd3738d423176fc5e0aa1b3c72a06a049414752ed668238af0\" alt=\"t equals 12\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/147e8b33e54502fb3500b7007066106821e74f72cb4aac0738df62b8ec709783\" alt=\"t equals 24\"></span>. The slope of the line of best fit is the difference in <span class=\"italic\">d</span>-values divided by the difference in <span class=\"italic\">t</span>-values, which gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/74ee0115baa3d484af293c19f397f5b3a13fb2da04164a2f0effd8478dee4444\" alt=\"the fraction with numerator 880 minus 480, and denominator 24 minus 12, end fraction, equals, the fraction 400 over 12\"></span>, or approximately 33. Writing the equation of the line of best fit in slope-intercept form gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e7cc5fecadd9d8351132d04be6c292a8a01fa095f235d3bf45779753d21de5e6\" alt=\"d equals, 33 t plus b\"></span>, where <span class=\"italic\">b</span> is the <span class=\"italic\">y</span>-coordinate of the <span class=\"italic\">y</span>-intercept. This equation is satisfied by all points on the line, so <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ffc50d80c00722927e78fbf20f7112a93069c71958184dde70a47d6bfc2166d2\" alt=\"d equals 480\"></span> when <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/191b9de50249c5cd3738d423176fc5e0aa1b3c72a06a049414752ed668238af0\" alt=\"t equals 12\"></span>. Thus, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dde3a3537505d95ec792ac77a727a54ce58448613522759784ec2a77118d3a54\" alt=\"480 equals, 33 times 12, plus b\"></span>, which is equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/38b327697a63f6e244f71632d12f59dd279dcb9343b2ff2695b1286cccee3afa\" alt=\"480 equals, 396 plus b\"></span>. Subtracting 396 from both sides of this equation gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2c2fc3c9f8375848797ed13aee519dd00f7bd11f7b4fffe49e4fae3dd38aff5b\" alt=\"b equals 84\"></span>. Therefore, an equation for the line of best fit could be <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/98ee4e8db78b05ec3b631c2556af8533f9e0476b313b8be4fecb42f37a4c29a2\" alt=\"d equals, 33 t plus 84\"></span>.</p><p>Choice A is incorrect and may result from an error in calculating the slope and misidentifying the <span class=\"italic\">y</span>-coordinate of the <span class=\"italic\">y</span>-intercept of the graph as the value of <span class=\"italic\">d</span> at <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/17e18e31840adb22a613d347a45c5f05f0196444445970139a0ed6685ed699e2\" alt=\"\"></span> rather than the value of <span class=\"italic\">d</span> at <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/03be3f9ca86e73f91aae3da5f4c70ddbd7015f7b2182c3cada4a3b84a54d9546\" alt=\"t equals 0\"></span>. Choice B is incorrect and may result from using the smallest value of <span class=\"italic\">t</span> on the graph as the slope and misidentifying the <span class=\"italic\">y</span>-coordinate of the <span class=\"italic\">y</span>-intercept of the graph as the value of <span class=\"italic\">d</span> at <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/17e18e31840adb22a613d347a45c5f05f0196444445970139a0ed6685ed699e2\" alt=\"t equals 10\"></span> rather than the value of <span class=\"italic\">d</span> at <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/03be3f9ca86e73f91aae3da5f4c70ddbd7015f7b2182c3cada4a3b84a54d9546\" alt=\"t equals 0\"></span>. Choice C is incorrect and may result from misidentifying the <span class=\"italic\">y</span>-coordinate of the <span class=\"italic\">y</span>-intercept as the smallest value of <span class=\"italic\">d</span> on the graph.</p><p>&nbsp;</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.615000+00:00","source_updated_at":"2023-08-02T20:25:59.615000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/780e9d7fbf21f8d6fe427db2ee46dc2657c7d41967b6b9523e5ca5a4ac9237b8\" alt=\"d equals, 0 point 0 3 t plus 402\"></span></span></p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fa2b74c2577ba1da8fde73c9b9bdb8a7a12740c69948b09cdfcac91800e89327\" alt=\"d equals, 10 t plus 402\"></span></span></p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/da3800d33c872d80eebdd86052f84436b4d7f916d7639768a32a4bc1cecbb68f\" alt=\"d equals, 33 t plus 300\"></span></span></p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/98ee4e8db78b05ec3b631c2556af8533f9e0476b313b8be4fecb42f37a4c29a2\" alt=\"d equals, 33 t plus 84\"></span></span></p>\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}}