{"id":"cb_question_bank:5fe31180-2a3c-4cfd-8906-a6787f8b6cbe","source_id":"cb_question_bank","source_item_id":"5fe31180-2a3c-4cfd-8906-a6787f8b6cbe","external_id":"658ecb3f-b141-4d7a-abcb-105abef728e2","ibn":null,"question_id":"05bb1af9","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.C.","skill":"Linear equations in two variables","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The line slants gradually down from left to right. The line passes through the following points: (negative 8 comma 4) (0 comma 2) (8 comma 0) The graph of y equals f left parenthesis x right parenthesis plus 14 is shown. Which equation defines function f ?","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 \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \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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The graph of y=fx+14 is shown. Which equation defines function f\n?

","rationale_html":"

Choice A is correct. An equation for the graph shown 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 the graph and its y-intercept is 0,b. Since the y-intercept of the graph shown is 0,2, the value of b\n is 2\n. Since the graph also passes through the point 4,1, the slope can be calculated as 1-24-0, or \n\t-\n\t\n\t\t1\n\t\t4\n\t\n\n. Therefore, the value of m\n is \n\t-\n\t\n\t\t1\n\t\t4\n\t\n\n. Substituting \n\t-\n\t\n\t\t1\n\t\t4\n\t\n\n for m\n and 2\n for b\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=-14x+2. It’s given that an equation for the graph shown is y=fx+14. Substituting fx+14 for y\n in the equation y=-14x+2  yields fx+14=-14x+2. Subtracting 14\n from both sides of this equation yields fx=-14x-12.

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

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

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

","correct_answer":["A"],"has_media":true,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.814000+00:00","source_updated_at":"2023-08-02T20:25:59.814000+00:00","options":[{"label":"A","content_html":"

fx=\n\t-\n\t\n\t\t1\n\t\t4\n\t\n\n\n\tx\n\t-\n\t12\n\n

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

fx=\n\t-\n\t\n\t\t1\n\t\t4\n\t\n\n\n\tx\n\t+\n\t16\n\n

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

fx=\n\t-\n\t\n\t\t1\n\t\t4\n\t\n\n\n\tx\n\t+\n\t2\n\n

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

fx=\n\t-\n\t\n\t\t1\n\t\t4\n\t\n\n\n\tx\n\t-\n\t14\n\n

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