{"id":"cb_question_bank:3552d49e-1579-4bc4-b9b1-0b6f4e113fa3","source_id":"cb_question_bank","source_item_id":"3552d49e-1579-4bc4-b9b1-0b6f4e113fa3","external_id":"803e7a6a-e220-4562-862c-82f2d02fcb7f","ibn":null,"question_id":"9f3cb472","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.C.","skill":"Linear equations in two variables","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Line t in the xy -plane has a slope of negative one third and passes through the point left parenthesis 9 comma 10 right parenthesis . Which equation defines line t ?","stimulus":"","stimulus_html":null,"stem_html":"

Line t\n in the xy-plane has a slope of \n\t-\n\t\n\t\t1\n\t\t3\n\t\n\n and passes through the point 9,10. Which equation defines line t\n?

","rationale_html":"

Choice D is correct. The equation that defines line t\n in the xy-plane can be written in slope-intercept form \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n, where m\n is the slope of line t\n and 0,b is its y-intercept. It’s given that line t\n has a slope of \n\t-\n\t\n\t\t1\n\t\t3\n\t\n\n. Therefore, \n\tm\n\t=\n\t\n\t\t-\n\t\t\n\t\t\t1\n\t\t\t3\n\t\t\n\t\n\n. Substituting \n\t-\n\t\n\t\t1\n\t\t3\n\t\n\n for m\n in the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n yields y=-13x+b, or \n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t\n\t\t\t\tx\n\t\t\t\t3\n\t\t\t\n\t\t\n\t\t+\n\t\tb\n\t\n\n. It’s also given that line t\n passes through the point 9,10. Substituting 9\n for x\n and 10\n for y\n in the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t\n\t\t\t\tx\n\t\t\t\t3\n\t\t\t\n\t\t\n\t\t+\n\t\tb\n\t\n\n yields 10=-93+b, or 10=-3+b. Adding 3\n to both sides of this equation yields \n\t13\n\t=\n\tb\n\n. Substituting 13\n for b\n in the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t\n\t\t\t\tx\n\t\t\t\t3\n\t\t\t\n\t\t\n\t\t+\n\t\tb\n\t\n\n yields \n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t\n\t\t\t\tx\n\t\t\t\t3\n\t\t\t\n\t\t\n\t\t+\n\t\t13\n\t\n\n.

\n

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

\n

Choice B is incorrect. This equation defines a line that has a slope of 9\n, not \n\t-\n\t\n\t\t1\n\t\t3\n\t\n\n, and passes through the point 0,10, not 9,10.

\n

Choice C is incorrect. This equation defines a line that passes through the point 0,10, not 9,10.

","correct_answer":["D"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.816000+00:00","source_updated_at":"2023-08-02T20:25:59.816000+00:00","options":[{"label":"A","content_html":"

\n\ty\n\t=\n\t\n\t\t\n\t\t\t13\n\t\t\tx\n\t\t\n\t\t-\n\t\t\n\t\t\t1\n\t\t\t3\n\t\t\n\t\n\n

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

\n\ty\n\t=\n\t\n\t\t\n\t\t\t9\n\t\t\tx\n\t\t\n\t\t+\n\t\t10\n\t\n\n

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

\n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t\n\t\t\t\tx\n\t\t\t\t3\n\t\t\t\n\t\t\n\t\t+\n\t\t10\n\t\n\n

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

\n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t\n\t\t\t\tx\n\t\t\t\t3\n\t\t\t\n\t\t\n\t\t+\n\t\t13\n\t\n\n

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