{"id":"cb_question_bank:32801e2c-27a5-489f-975e-3952ab9d5f7c","source_id":"cb_question_bank","source_item_id":"32801e2c-27a5-489f-975e-3952ab9d5f7c","external_id":"9b172c91-1885-4bc0-9faa-73425007e043","ibn":null,"question_id":"03a16790","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":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The scatterplot shows the relationship between two variables, x and y . A line of best fit is also shown. The scatterplot has 10 data points. The data points are in a linear pattern trending down from left to right. A line of best fit is shown: The line of best fit slants down from left to right. 2 points are touching the line of best fit. 3 points are above the line of best fit. 5 points are below the line of best fit. The line of best fit passes through the following approximate coordinates: (0 comma 12.9) (6 comma 8) (12 comma 3.2) Which of the following is closest to the slope of the line of best fit shown?","stimulus":"","stimulus_html":null,"stem_html":"

The scatterplot shows the relationship between two variables, x\n and y\n. A line of best fit is also shown.

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\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

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Which of the following is closest to the slope of the line of best fit shown?

","rationale_html":"

Choice B is correct. A line of best fit is shown in the scatterplot such that as the value of x\n increases, the value of y\n decreases. Thus, the slope of the line of best fit shown is negative. The slope of a line passing through two points, x1,y1 and x2,y2, can be calculated as y2-y1x2-x1. The line of best fit shown passes approximately through the points 1,12 and 11,4. Substituting 1,12 and 11,4 for x1,y1 and x2,y2, respectively, in y2-y1x2-x1 gives 4-1211-1, which is equivalent to -810, or -0.8. Therefore, of the given choices, -0.8 is closest to the slope of the line of best fit shown.

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Choice A is incorrect and may result from conceptual or calculation errors.

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Choice C is incorrect. The line of best fit shown has a negative slope, not a positive slope.

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Choice D is incorrect. The line of best fit shown has a negative slope, not a positive slope.

","correct_answer":["B"],"has_media":true,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.834000+00:00","source_updated_at":"2023-08-02T20:25:59.834000+00:00","options":[{"label":"A","content_html":"

-2.4\n

","ord":0},{"label":"B","content_html":"

-0.8\n

","ord":1},{"label":"C","content_html":"

0.8\n

","ord":2},{"label":"D","content_html":"

2.4\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}}