The graph of the function f is a line in the xy -plane. If the line has slope and ,

Question

The graph of the function f is a line in the xy -plane. If the line has slope and , which of the following defines f ?

Accepted Answer

Choice B is correct. The equation for the function f in the xy -plane can be represented by , where m is the slope and b is the y -coordinate of the y -intercept. Since it&rsquo;s given that the line has a slope of , it follows that in , which yields . It&rsquo;s given that . This implies that the graph of the function f in the xy -plane passes through the point . Thus, the y -coordinate of the y -intercept of the graph is 3, so in , which yields . Therefore, the equation defines the function f. Choice A is incorrect and may result from a sign error for the y -intercept. Choice C is incorrect and may result from using the denominator of the given slope as m in , in addition to a sign error for the y -intercept. Choice D is incorrect and may result from using the denominator of the given slope as m in .

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