{"id":"cb_question_bank:4c077efb-cb9e-4f91-8f16-bcff26f3bee1","source_id":"cb_question_bank","source_item_id":"4c077efb-cb9e-4f91-8f16-bcff26f3bee1","external_id":"d243de3a-1370-41b8-a350-5396b80263a0","ibn":null,"question_id":"5cf1bbc9","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The graph of the function f , where y = f ( x ) , gives the total cost y , in dollars, for a certain video game system and x games. What is the best interpretation of the slope of the graph in this context?","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

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The graph of the function f\n, where y=f(x), gives the total cost y\n, in dollars, for a certain video game system and x\n games. What is the best interpretation of the slope of the graph in this context?

","rationale_html":"

Choice A is correct. The given graph is a line, and the slope of a line is defined as the change in the value of y\n for each increase in the value of x\n by 1\n. It’s given that y\n represents the total cost, in dollars, and that x\n represents the number of games. Therefore, the change in the value of y\n for each increase in the value of x\n by 1\n represents the change in total cost, in dollars, for each increase in the number of games by 1\n. In other words, the slope represents the cost, in dollars, per game. The graph shows that when the value of x\n increases from 0\n to 1\n, the value of y\n increases from 100\n to 125\n. It follows that the slope is 25\n, or the cost per game is $25. Thus, the best interpretation of the slope of the graph is that each game costs $25.

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Choice B is incorrect. This is an interpretation of the y-intercept of the graph rather than the slope of the graph.

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Choice C is incorrect. The slope of the graph is the cost per game, not the cost of the video game system.

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Choice D is incorrect. Each game costs $25, not $100.

","correct_answer":["A"],"has_media":true,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.811000+00:00","source_updated_at":"2023-08-02T20:25:59.811000+00:00","options":[{"label":"A","content_html":"

Each game costs $25\n.

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

The video game system costs $100\n.

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

The video game system costs $25\n.

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

Each game costs $100\n.

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