Answer
$a.\quad 4$
$b.\quad y=4x-8$
Work Step by Step
Average rate of change from $a$ to $b$
$=\displaystyle \frac{\Delta y}{\Delta x}=\frac{f(b)-f(a)}{b-a},\quad a\neq b$
The average rate of change of a function from $a$ to $b$ equals the slope of the secant line containing the two points $(a,f(a))$ and $(b,f(b))$ on its graph.
$m_{sec}=\displaystyle \frac{f(b)-f(a)}{b-a}$
---
$a.$
$h(4)=8, \quad h(2)=0$
Average rate of change of $h$ from $2$ to $4$:
$\displaystyle \frac{h(4)-h(2)}{4-2}=\frac{8-0}{2}=4$
$b.$
We have slope $m=4$ and a point $(2,0)$.
Point-slope equation of the secant:
$y-y_{1}=m(x-x_{1})$
$y-0=4(x-2)$
$y=4x-8$
