For the linear function f , the graph of y = f ( x ) in the xy -plane has

Question

For the linear function f , the graph of y = f ( x ) in the xy -plane has a slope of 39 and passes through the point 0 , 0 . Which equation defines f ?

Accepted Answer

Choice D is correct. An equation defining a linear function 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. It&rsquo;s given that the graph of y = f x has a slope of 39 , so m = 39 . It&rsquo;s also given that the graph of y = f x passes through the point 0 , 0 , so b = 0 . Substituting 39 for m and 0 for b in f x = m x + b yields f x = 39 x + 0 , or f x = 39 x . Thus, the equation that defines f is f x = 39 x . Choice A is incorrect. This equation defines a function whose graph has a slope of - 39 , not 39 . Choice B is incorrect. This equation defines a function whose graph has a slope of 1 39 , not 39 . Choice C is incorrect. This equation defines a function whose graph has a slope of 1 , not 39 , and passes through the point 0 , - 39 , not 0 , 0 .

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