{"id":"cb_question_bank:c49f47ba-1a9a-4fd1-9bd3-28195e8f2186","source_id":"cb_question_bank","source_item_id":"c49f47ba-1a9a-4fd1-9bd3-28195e8f2186","external_id":null,"ibn":"026242-DC","question_id":"9eb896c5","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":"Which of the following could be the equation for a line of best fit for the data shown in the scatterplot above?","stimulus":"The figure presents a scatterplot in the first quadrant of the x y plane. The numbers 0 through 10, in increments of 2, are indicated on the x axis. The numbers 0 through 30, in increments of 5, are indicated on the y axis. There are 8 data points in the scatterplot. The data points begin at the point with approximate coordinates 1 comma 4, and trend upward and to the right until they end at the point with approximate coordinates 8 comma 26.","stimulus_html":"
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\n \"The
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Which of the following could be the equation for a line of best fit for the data shown in the scatterplot above?

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Choice A is correct. The data show a strong linear relationship between x and y. The line of best fit for a set of data is a linear equation that minimizes the distances from the data points to the line. An equation for the line of best fit can be written in slope-intercept form, \"y, where m is the slope of the graph of the line and b is the y-coordinate of the y-intercept of the graph. Since, for the data shown, the y-values increase as the x-values increase, the slope of a line of best fit must be positive. The data shown lie almost in a line, so the slope can be roughly estimated using the formula for slope, \"m. The leftmost and rightmost data points have coordinates of about \"1 and \"8, so the slope is approximately \"the, which is a little greater than 3. Extension of the line to the left would intersect the y-axis at about \"the. Only choice A represents a line with a slope close to 3 and a y-intercept close to \"the.

Choice B is incorrect and may result from switching the slope and y-intercept. The line with a y-intercept of \"0 and a slope of 0.8 is farther from the data points than the line with a slope of 3 and a y-intercept of \"0. Choices C and D are incorrect. They represent lines with negative slopes, not positive slopes.

\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":"

\n \n \"y\n

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\n \n \"y\n

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\n \n \"y\n

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\n \n \"y\n

\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}}