jmc

Since the line passes through $(4,-8)$, we know the equation will be satisfied when we plug in $x=4$ and $y=-8$. This gives

$$\begin{array}{rl}a(4)+(a+1)(-8)& =a+2\\ 4a-8a-8& =a+2\\ -4a-8& =a+2\\ -10& =5a\\ -2& =a.\end{array}$$Thus $a=\boxed{-2}$. The equation is $-2x-y=0$, or $y=-2x$, and we can see that $(4,-8)$ lies along this line.