Answer
$a.\quad 1$
$b.\quad y=x+3$
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.
$m_{sec}=\displaystyle \frac{f(b)-f(a)}{b-a}$
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$a.$
$g(2)=5, \quad g(-1)=2$
Average rate of change of $g$ from -1 to 2:
$\displaystyle \frac{g(2)-g(-1)}{2-(-1)}=\frac{5-2}{3}=\frac{3}{3}=1$
$b.$
We have slope $m=1$ and a point $(2,5)$.
Point-slope equation of the secant:
$y-y_{1}=m(x-x_{1})$
$y-5=(x-2)$
$y=x-2+5$
$y=x+3$
