jmc

First, remember that the slope of a line in the form of $y=mx+b$ is equal to $m$. So, the line must take the form $y=-7x+b$. Next, substitute the point $(3,0)$ and solve for $b$: $$\begin{array}{rl}0& =-7(3)+b\\ \Rightarrow 0& =-21+b\\ \Rightarrow 21& =b\end{array}$$ Therefore, the value of $m+b$ is $-7+21=\boxed{14}$.