For the linear function f , f 0 = 17 and f 1 = 17 . Which equation defines f

Question

For the linear function f , f 0 = 17 and f 1 = 17 . Which equation defines f ?

Accepted Answer

Choice C is correct. An equation defining the linear function f can be written in the form f x = m x + b , where m is the slope and 0 , b is the y -intercept of the graph of y = f x in the xy -plane. The slope of the graph of y = f x can be found using the formula m = y 2 - y 1 x 2 - x 1 , where x 1 , y 1 and x 2 , y 2 are any two points that the graph passes through. If f 0 = 17 , it follows that the graph of y = f x passes through the point 0 , 17 . If f 1 = 17 , it follows that the graph of y = f x passes through the point 1 , 17 . Substituting 0 , 17 and 1 , 17 for x 1 , y 1 and x 2 , y 2 , respectively, in the formula m = y 2 - y 1 x 2 - x 1 yields m = 17 - 17 1 - 0 , which is equivalent to m = 0 1 , or m = 0 . Since the graph of y = f x passes through 0 , 17 , it follows that b = 17 . Substituting 0 for m and 17 for b in the equation f x = m x + b yields f x = 0 x + 17 , or f x = 17 . Thus, the equation that defines f is f x = 17 . Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.

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