**Answer:**

Part A)

Part B) The distance between the y-intercepts is equal to 4 units

Part C) The value of h(x) will always be greater than the value of m(x) for any value of x

**Step-by-step explanation:**

**Part A)** What is the value of h(4) -m(16)

we have

For x=4

Find the equation of the line m(x)

**Find the slope**

take the points

(8,2) and (12,4)

The formula to calculate the slope between two points is equal to

substitute

**Find the equation of the line in slope intercept form**

we have

substitute

solve for b

therefore

**Find m(16)**

so

**Part B)** we know that

The y-intercept is the value of y when the value of x is equal to zero

**Find the y-intercept of h(x)**

For x=0

**Find the y-intercept of m(x)**

For x=0

therefore

The distance between the y-intercepts is equal to 2-(-2)=4 units

**Part C)**

Graph both equations

using a graphing tool

see the attached figure

The value of h(x) will always be greater than the value of m(x) for any value of x

If your question is not fully disclosed, then try using the search on the site and find other answers on the subject Mathematics.

Find another answersMathematics, published 11.05.2023

Mathematics, published 23.03.2023

Use the equation to identify the center and radius of the circle (X+3)^2+(y-7^2=11

Mathematics, published 27.05.2023