In the linear function h , h ( 28 ) = 15 and h ( 26 ) = 22 .

Question

In the linear function h , h ( 28 ) = 15 and h ( 26 ) = 22 . Which equation defines h ?

Accepted Answer

Choice D is correct. An equation defining h can be written in the form y = m x + b , where y = h x , m represents the slope of the graph of y = h x in the xy -plane, and b represents the y -coordinate of the y -intercept of the graph. It&rsquo;s given that h 28 = 15 and h 26 = 22 . It follows that the points 28 , 15 and 26 , 22 are on the graph of y = h x in the xy -plane. The slope can be found by using any two points, x 1 , y 1 and x 2 , y 2 , and the formula m = y 2 - y 1 x 2 - x 1 . Substituting 28 , 15 and 26 , 22 for x 1 , y 1 and x 2 , y 2 , respectively, in the slope formula yields m = 22 - 15 26 - 28 , or m = - 7 2 . Substituting - 7 2 for m and 28 , 15 for x , y in the equation y = m x + b yields 15 = - 7 2 28 + b , or 15 = - 98 + b . Adding 98 to both sides of this equation yields 113 = b . Substituting - 7 2 for m and 113 for b in the equation y = m x + b yields y = - 7 2 x + 113 . Since y = h x , it follows that the equation that defines h is h x = - 7 2 x + 113 . Choice A is incorrect. For this function, h 26 = 109 7 , not h 26 = 22 . Choice B is incorrect. For this function, h 28 = 105 , not h 28 = 15 , and h 26 = 739 7 , not h 26 = 22 . Choice C is incorrect. For this function, h 28 = - 75 , not h 28 = 15 , and h 26 = - 68 , not h 26 = 22 .

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