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