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 2 and has a y -intercept at 0 , - 5 . Which equation defines f ?

Accepted Answer

Choice D 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. It&rsquo;s given that the graph of y = f x has a slope of 2 . Therefore, m = 2 . It&rsquo;s also given that the graph of y = f x has a y -intercept at 0 , - 5 . Therefore, b = - 5 . Substituting 2 for m and - 5 for b in the equation f x = m x + b yields f x = 2 x - 5 . Thus, the equation that defines f is f x = 2 x - 5 . Choice A is incorrect. For this function, the graph of y = f x in the xy -plane has a slope of 1 2 , not 2 . Choice B is incorrect. For this function, the graph of y = f x in the xy -plane has a slope of - 1 2 , not 2 . Choice C is incorrect. For this function, the graph of y = f x in the xy -plane has a slope of - 2 , not 2 .

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