In the xy -plane, the graph of the linear function f contains the points 0 , 3 and 7 ,

Question

In the xy -plane, the graph of the linear function f contains the points 0 , 3 and 7 , 31 . Which equation defines f , where y = f x ?

Accepted Answer

Choice C is correct. In the xy -plane, an equation of the graph of a linear function can be written in the form f x = m x + b , where m represents the slope and 0 , b represents the y -intercept of the graph of y = f x . It&rsquo;s given that the graph of the linear function f , where y = f x , in the xy -plane contains the point 0 , 3 . Thus, b = 3 . The slope of the graph of a line containing any two points x 1 , y 1 and x 2 , y 2 can be found using the slope formula, m = y 2 - y 1 x 2 - x 1 . Since it&rsquo;s given that the graph of the linear function f contains the points 0 , 3 and 7 , 31 , it follows that the slope of the graph of the line containing these points is m = 31 - 3 7 - 0 , or m = 4 . Substituting 4 for m and 3 for b in f x = m x + b yields f x = 4 x + 3 . Choice A is incorrect. This function represents a graph with a slope of 28 and a y -intercept of 0 , 34 . Choice B is incorrect. This function represents a graph with a slope of 3 and a y -intercept of 0 , 38 . Choice D is incorrect. This function represents a graph with a slope of 7 and a y -intercept of 0 , 3 .

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