Question

the function h is defined by h(x)=4x+28. the graph of y=h(z) 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?

Answer 1

The x-intercept (a) is -7, and the y-intercept (b) is 28. Adding these together, a + b equals 21.

Step-by-step explanation:

To find the x-intercept and y-intercept of the function h(x) = 4x + 28, we set each variable to zero in turn and solve for the other variable.

For the y-intercept (b), we set x = 0:

h(0) = 4(0) + 28

= 28

So, the y-intercept is at the point (0, 28), which means b = 28.

For the x-intercept (a), we set h(x) = 0:

0 = 4x + 28

4x = -28

x = -7

So, the x-intercept is at the point (-7, 0), which means a = -7.

The question asks for the sum of a + b. We have a = -7 and b = 28.

a + b = -7 + 28 = 21

Therefore, the value of a + b is 21.