jmc

Since $\alpha$ is inversely proportional to $\beta$, by definition $\alpha \beta =k$ for some constant $k$. Plugging in, we see that $4\cdot 9=k$, so $k=36$. So when $\beta =-72$, we have that $-72\alpha =36$, or $\alpha =\boxed{-\frac{1}{2}}$.