### Instruction: Suppose that $\alpha$ is inversely proportional to $\beta$.  If $\alpha = 4$ when $\beta = 9$, find $\alpha$ when $\beta = -72$.### Response: So we know that if two variables are inversely proportional then their product is constant.
That means that $alpha*beta = 4*9 = 36$ for all values of $alpha$ and $beta$.
Right. So when $beta = -72$, then $alpha*(-72) = 36$.
Dividing both sides by $-72$ gives $alpha = -36/72 = -1/2$.