Suppose that $\alpha$ is inversely proportional to $\beta$. If $\alpha = -3$ when $\beta = -6$, find $\alpha$ when $\beta = 8$. Express your answer as a fraction.
a = k / b
-3 = k / -6
k = proportionality constant = 18
a = 18/b
a = 18/8 = 2 1/4 or 9/4