For the linear function h , the graph of y = h x in the xy -plane passes through the

Question

For the linear function h , the graph of y = h x in the xy -plane passes through the points 7 , 21 and 9 , 25 . Which equation defines h ?

Accepted Answer

Choice B is correct. It&rsquo;s given that the graph of the linear function h , where y = h x , passes through the points 7 , 21 and 9 , 25 in the xy -plane. 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 in the xy -plane, and b represents the y -coordinate of the y -intercept of the graph. The slope can be found 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 7 , 21 and 9 , 25 for x 1 , y 1 and x 2 , y 2 , respectively, in the slope formula yields m = 25 - 21 9 - 7 , which is equivalent to m = 4 2 , or m = 2 . Substituting 2 for m and 7 , 21 for x , y in the equation y = m x + b yields 21 = 2 7 + b , or 21 = 14 + b . Subtracting 14 from each side of this equation yields 7 = b . Substituting 2 for m and 7 for b in the equation y = m x + b yields y = 2 x + 7 . Since y = h x , it follows that the equation that defines h is h x = 2 x + 7 . Choice A is incorrect. For this function, the graph of y = h x in the xy -plane would pass through 7 , 0 , not 7 , 21 , and 9 , 1 , not 9 , 25 . Choice C is incorrect. For this function, the graph of y = h x in the xy -plane would pass through 7 , 70 , not 7 , 21 , and 9 , 84 , not 9 , 25 . Choice D is incorrect. For this function, the graph of y = h x in the xy -plane would pass through 7 , 88 , not 7 , 21 , and 9 , 106 , not 9 , 25 .

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