{"id":"cb_question_bank:283dbc1e-12d1-426d-a74f-8481d22d767c","source_id":"cb_question_bank","source_item_id":"283dbc1e-12d1-426d-a74f-8481d22d767c","external_id":"57cffc23-e07d-4acc-9f42-b8eacfd50cd8","ibn":null,"question_id":"2e74e403","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":"In the given scatterplot, a line of best fit for the data is 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. 5 points are touching the line of best fit. 2 points are above the line of best fit. 3 points are below the line of best fit. The line of best fit passes through the following approximate coordinates: (1 comma 7) (4 comma 5) (10 comma 1) Which of the following is closest to the slope of this line of best fit?","stimulus":"","stimulus_html":null,"stem_html":"

In the given scatterplot, a line of best fit for the data is 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 \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \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 this line of best fit?

","rationale_html":"

Choice C 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. It follows that the slope of the line of best fit shown is negative. The slope of a line in the xy-plane that passes through the points x1,y1 and x2,y2 can be calculated as y2-y1x2-x1. The line of best fit shown passes approximately through the points 0,8 and 10,1. Substituting 0,8 for x1,y1 and 10,1 for x2,y2 in y2-y1x2-x1 yields the slope of the line being approximately 1-810-0, which is equivalent to -710, or -0.7. Therefore, of the given choices, -0.7 is the closest to the slope of this line of best fit.

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

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

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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":"

7\n

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

0.7\n

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

-0.7\n

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

-7\n

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