Direction of slope change when axes are swapped

Three data points are $(x,y)=(5,5)$, $(4,0)$ and $(6,10)$. You fit $y$ on $x$ and record the slope, then fit $x$ on $y$. Does the slope go up, stay the same or go down? Answer $1$, $0$ or $-1$ respectively.

$-1$ (it falls). Both slopes share the covariance in the numerator but divide by the variance of the regressor. The $y$ values are far more spread out than the $x$ values, so the second slope is smaller (here $5$ drops to $0.2$).