{"id":"cb_question_bank:8e176d11-624a-467c-bc07-bf73bad42b18","source_id":"cb_question_bank","source_item_id":"8e176d11-624a-467c-bc07-bf73bad42b18","external_id":null,"ibn":"026150-DC","question_id":"3c5b19ef","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":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The scatterplot above shows the number of visitors to a railroad museum in Pennsylvania each year from 1968 to 1980, where t is the number of years since 1968 and n is the number of visitors. A line of best fit is also shown. Which of the following could be an equation of the line of best fit shown?","stimulus":"The figure presents a scatterplot titled “Railroad Museum Visitors.” The horizontal axis is labeled “Years since 1968,” and the numbers 0 through 15, in increments of 5, are indicated. The vertical axis is labeled “Annual visitors,” and the numbers 0 through 80,000, in increments of 20,000, are indicated. There are 13 data points indicated on the scatterplot. The data points begin at the point with approximate coordinates 0 comma 5,000, and trend upward and to the right until they end at the point with approximate coordinates 12 comma 75,000. A line of best fit is drawn. The line begins at the point with approximate coordinates 0 comma 16,000, and slants upward and to the right. It passes through the point with approximate coordinates 5 comma 40,000, and continues upward until it ends at the point with approximate coordinates 12 comma 74,000.","stimulus_html":"<div class=\"stimulus_reference \">\n        <div class=\"standalone_image \">\n          <img src=\"/api/assets/60df013ba6052bced2dac1816ccb88004b2babd6c9fa9a44312bd0096c3450b0\" alt=\"The figure presents a scatterplot titled “Railroad Museum Visitors.” The horizontal axis is labeled “Years since 1968,” and the numbers 0 through 15, in increments of 5, are indicated. The vertical axis is labeled “Annual visitors,” and the numbers 0 through 80,000, in increments of 20,000, are indicated. There are 13 data points indicated on the scatterplot. The data points begin at the point with approximate coordinates 0 comma 5,000, and trend upward and to the right until they end at the point with approximate coordinates 12 comma 75,000. A line of best fit is drawn. The line begins at the point with approximate coordinates 0 comma 16,000, and slants upward and to the right. It passes through the point with approximate coordinates 5 comma 40,000, and continues upward until it ends at the point with approximate coordinates 12 comma 74,000.\" width=\"182\" height=\"136\"></div>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">The scatterplot above shows the number of visitors to a railroad museum in Pennsylvania each year from 1968 to 1980, where <span class=\"italic\">t</span> is the number of years since 1968 and <span class=\"italic\">n</span> is the number of visitors. A line of best fit is also shown. Which of the following could be an equation of the line of best fit shown?</p>\n","rationale_html":"<p>Choice A is correct. An equation of a line of best fit can be written in the form <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f4904e8b3e40d4918a98953fa39c4c7777ddb3800b224a07ca1cb47cd3155e8b\" alt=\"y equals, a, plus b x\"></span>, where <span class=\"italic\">a</span> is the <span class=\"italic\">y</span>-intercept of the line and <span class=\"italic\">b</span> is the slope. In the scatterplot shown, the line of best fit intersects the <span class=\"italic\">y</span>-axis just over halfway between 10,000 and 20,000, or approximately 16,000. The line of best fit also intersects the graph at <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/397bed232c5a9148a1785418b3091630ecdd0446561264246baaf0b092dac47f\" alt=\"the point with coordinates 5 comma 40,000 \"></span>. Using the slope formula <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/df175016b5d19540cebbcefeafbeaf6288b688f6cd41952fa65ec47cc03f6826\" alt=\"b equals, the fraction with numerator y sub 2 minus y sub 1, and denominator x sub 2 minus x sub 1, end fraction\"></span> and two points that lie on the graph such as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/397bed232c5a9148a1785418b3091630ecdd0446561264246baaf0b092dac47f\" alt=\"the point with coordinates 5 comma 40,000 \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4579101507deee29a0ce23b7b2dd0aa53b9ce21dbbb2e9fc4eba844ad3535417\" alt=\"the point with coordinates 0 comma 16,000 \"></span>, the slope can be approximated as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/61fcd6b56e1d9970b0d7c7f5ce41dce69a3a035cd16e884f4a61ce3b441c9e4e\" alt=\"the fraction with numerator 40,000 minus 16,000, and denominator 5 minus 0, end fraction\"></span>, or 4,800. Only choice A has a <span class=\"italic\">y</span>-intercept near the estimate of 16,000 and a slope near the estimate of 4,800. Therefore, an equation of the line of best fit could be <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8c8c39cc23347047a590e245c41fb1e6bff56ce6ebfdd1d576acc24d96a4cee0\" alt=\"n equals, 16,090 plus 4,680 t\"></span>.<span class=\"italic\"></span></p><p>Choice B is incorrect because the values for the slope and the <span class=\"italic\">y</span>-coordinate of the <span class=\"italic\">y</span>-intercept are switched. Choice C is incorrect because the value for the slope is approximately double the actual slope. Choice D is incorrect because the values for the slope and the <span class=\"italic\">y-</span>intercept are switched and because the slope is approximately double the actual slope.</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.620000+00:00","source_updated_at":"2023-08-02T20:25:59.620000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8c8c39cc23347047a590e245c41fb1e6bff56ce6ebfdd1d576acc24d96a4cee0\" alt=\"n equals, 16,090, plus 4,680, t\"></span></span>\n          </p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a5c3a8751e36dfc26da3767ee5bc3cc7beb11736c88964c6609b339682d4b0e6\" alt=\"n equals, 4,690, plus 16,090, t\"></span></span>\n          </p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5e3382292ec444a850d94ff1df5b41ce896562eb8beb5b72ffe1501e1637cb98\" alt=\"n equals, 16,090, plus 9,060, t\"></span></span>\n          </p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ec58e4614747a3a3263b2886c1f0233e3449e44fd14aeb5a841c79a623777b75\" alt=\"n equals, 9,060, plus 16,090, t\"></span></span>\n          </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}}