The function h is defined by h x = 4 x + 28 . The graph of y = h

Question

The function h is defined by h x = 4 x + 28 . The graph of y = h x in the xy -plane has an x -intercept at a , 0 and a y -intercept at 0 , b , where a and b are constants. What is the value of a + b ?

Accepted Answer

Choice A is correct. The x -intercept of a graph in the xy -plane is the point on the graph where y = 0 . It's given that function h is defined by h x = 4 x + 28 . Therefore, the equation representing the graph of y = h x is y = 4 x + 28 . Substituting 0 for y in the equation y = 4 x + 28 yields 0 = 4 x + 28 . Subtracting 28 from both sides of this equation yields - 28 = 4 x . Dividing both sides of this equation by 4 yields - 7 = x . Therefore, the x -intercept of the graph of y = h x in the xy -plane is - 7 , 0 . It's given that the x -intercept of the graph of y = h x is a , 0 . Therefore, a = - 7 . The y -intercept of a graph in the xy -plane is the point on the graph where x = 0 . Substituting 0 for x in the equation y = 4 x + 28 yields y = 4 0 + 28 , or y = 28 . Therefore, the y -intercept of the graph of y = h x in the xy -plane is 0 , 28 . It's given that the y -intercept of the graph of y = h x is 0 , b . Therefore, b = 28 . If a = - 7 and b = 28 , then the value of a + b is - 7 + 28 , or 21 . Choice B is incorrect. This is the value of b , not a + b . Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect. This is the value of - a + b , not a + b .

Question 77e2c7