jmc

The slope of the line through $(7,8)$ and $(9,0)$ is $\frac{8-0}{7-9}=\frac{8}{-2}=-4$. Thus, the line has equation $y=-4x+b$ for some $b$. Since $B(9,0)$ lies on this line, we have $0=-4(9)+b$, so $b=36$. Hence, the equation of the line is $y=-4x+36$, and the desired sum is $-4+36=\boxed{32}$.