Complete the following.

1. What is the average rate of change of the function $g\left(x\right) = 6 − 2x$ over the interval $[2, 6]$?

   Hint (a):

   $\frac{g(6) - g(2)}{6-2}$

2. Over the interval $[5, 7]$?

   Hint (b):

   $\frac{g(7) - g(5)}{7-5}$

3. Do you think it is true that $g\left(x\right)$ will have a constant average rate of change over any interval? Why or why not?

   Answer (c):

   Yes, because it is linear.

4. Prove your answer to part (c) by computing the average rate of change for $g\left(x\right)$ over the interval $[a, b]$.

   Hint (d):

   $\frac{g(b) - g(a)}{b-a} = \frac{6 - 2b - (6 - 2a)}{b - a} =$