{"id":"cb_question_bank:ca589945-b2cc-482d-b2c3-590ebfa8efef","source_id":"cb_question_bank","source_item_id":"ca589945-b2cc-482d-b2c3-590ebfa8efef","external_id":"0c969089-dec5-4180-9837-2658154630eb","ibn":null,"question_id":"5f3ee607","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":3,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The scatterplot has 10 data points. The data points are in a linear pattern trending down from left to right. Select data points have the following approximate coordinates: (0.8 comma 8.9) (2.8 comma 5.1) (4.1 comma 2.9) Which of the following equations is the most appropriate linear model for the data shown in the scatterplot?","stimulus":"","stimulus_html":null,"stem_html":"

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

\n

Which of the following equations is the most appropriate linear model for the data shown in the scatterplot?

","rationale_html":"

Choice B is correct. The equation representing a linear model can be written in the form y=a+bx, or y=bx+a, where b\n is the slope of the graph of the model and 0,a is the y-intercept of the graph of the model. The scatterplot shows that as the x-values of the data points increase, the y-values of the data points decrease, which means the graph of an appropriate linear model has a negative slope. Therefore, b<0. The scatterplot also shows that the data points are close to the y-axis at a positive value of y\n. Therefore, the y-intercept of the graph of an appropriate linear model has a positive y-coordinate, which means a>0. Of the given choices, only choice B, y=-1.9x+10.1, has a negative value for b\n, the slope, and a positive value for a\n, the y-coordinate of the y-intercept. 

\n

Choice A is incorrect. The graph of this model has a y-intercept with a negative y-coordinate, not a positive y-coordinate.

\n

Choice C is incorrect. The graph of this model has a positive slope, not a negative slope, and a y-intercept with a negative y-coordinate, not a positive y-coordinate.

\n

Choice D is incorrect. The graph of this model has a positive slope, not a negative 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":"

\n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t1.9\n\t\t\tx\n\t\t\n\t\t-\n\t\t10.1\n\t\n\n

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

\n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t1.9\n\t\t\tx\n\t\t\n\t\t+\n\t\t10.1\n\t\n\n

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

\n\ty\n\t=\n\t\n\t\t\n\t\t\t1.9\n\t\t\tx\n\t\t\n\t\t-\n\t\t10.1\n\t\n\n

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

\n\ty\n\t=\n\t\n\t\t\n\t\t\t1.9\n\t\t\tx\n\t\t\n\t\t+\n\t\t10.1\n\t\n\n

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