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

Question

For the function f , the graph of y = f ( x ) in the xy -plane has a slope of 3 and passes through the point 0 , - 8 . Which equation defines f ?

Accepted Answer

Choice B is correct. An equation defining a linear function can be written in the form f x = m x + b , where m and b are constants, m is the slope of the graph of y = f x in the xy -plane, and 0 , b is the y -intercept of the graph. It's given that for the function f , the graph of y = f x in the xy -plane has a slope of 3 . Therefore, m = 3 . It's also given that this graph passes through the point 0 , - 8 . Therefore, the y -intercept of the graph is 0 , - 8 , and it follows that b = - 8 . Substituting 3 for m and - 8 for b in the equation f x = m x + b yields f x = 3 x - 8 . Thus, the equation that defines f is f x = 3 x - 8 . Choice A is incorrect. For this function, the graph of y = f x in the xy -plane passes through the point 0 , 0 , not 0 , - 8 . Choice C is incorrect. For this function, the graph of y = f x in the xy -plane passes through the point 0 , 5 , not 0 , - 8 . Choice D is incorrect. For this function, the graph of y = f x in the xy -plane passes through the point 0 , 11 , not 0 , - 8 .

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