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3 For the linear function f, the graph of y = f x in ^ h the xy-plane has a slope of 7 and passes through the point 0,5. Which equation defines f? ^ h =
Correct answer: C (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice C is correct. An equation that defines a linear function f can be written in = + = the form f^xh mx b, where m is the slope of the graph of y f^xh in the 0, xy-plane and ^ bh is the y-intercept of the graph. It’s given that for the linear = = function f, the graph of y f^xh in the xy-plane has a slope of 7. Therefore, m 7. 34 SAT PRACTICE TEST #11 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 1 = It’s also given that the graph of y f^xh in the xy-plane passes through the 0,5 0,5 point ^ h. Therefore, the y-intercept of the graph is ^ h, and it follows that = = + b 5. Substituting 7 for m and 5 for b in the equation f^xh mx b yields =7 +5 f^xh x . Choice A is incorrect. This equation defines a function whose graph has a slope of 0,0 0,5 5, not 7, and passes through the point ^ h, not ^ h. Choice B is incorrect. This 35 equation defines a function whose graph has a slope of , not 7, and passes 0,0 0,5 through the point ^ h, not ^ h. Choice D is incorrect. This equation defines a 12 function whose graph has a slope of , not 7.
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