{"id":"cb_question_bank:f0292b5f-3705-4a8e-bb65-76b8efa19f66","source_id":"cb_question_bank","source_item_id":"f0292b5f-3705-4a8e-bb65-76b8efa19f66","external_id":"62f651c4-37e7-4fa9-8a3d-ff62ceb23066","ibn":null,"question_id":"39aa146d","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":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The scatterplot shows the relationship between x and y . A line of best fit is also shown. The scatterplot has 6 data points. The data points are in a linear pattern trending up from left to right. A line of best fit is shown: The line of best fit slants up from left to right. 1 point is touching the line of best fit. 2 points are above the line of best fit. 3 points are below the lines of best fit. The line of best fit passes through the following approximate coordinates: (0 comma 0.2) (4 comma 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 x\n and y\n. A line of best fit is also shown.

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

","rationale_html":"

Choice C is correct. It's given that the scatterplot shows the relationship between two variables, x\n and y\n, and a line of best fit is shown. For the line of best fit shown, for each increase in the value of x\n by 1\n, the corresponding value of y\n increases by a constant rate. It follows that the relationship between the variables x\n and y\n has a positive linear trend. A line in the xy-plane that passes through the points a,b and c,d has a slope of d-bc-a. The line of best fit shown passes approximately through the points 0,0.25 and 4,2. It follows that the slope of this line is approximately 2-0.254-0, which is equivalent to 0.4375\n. Therefore, of the given choices, 0.44\n is closest to the slope of the line of best fit shown.

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Choice A is incorrect. This is the slope of a line of best fit for a relationship between x\n and y\n that has a negative, rather than a positive, linear trend.

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Choice B is incorrect. This is the slope of a line of best fit for a relationship between x\n and y\n that has a negative, rather than a positive, linear trend.

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

","correct_answer":["C"],"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":"

-2.27\n

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

-0.44\n

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

0.44\n

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

2.27\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}}