jmc

We can quickly see that we can get a solution to the equation if the first fraction is 1 and the second is -1 which gives $(x,y)=(2,-3)$. Similarly if we let $(x,y)=(-2,3)$ we get the first fraction to be $-1$ and the second to be 1. The slope of the line through these two points is $\frac{-3-3}{2-(-2)}=\boxed{-\frac{3}{2}}$.