Slope when you regress x on y instead of y on x

Two variables have sample variances $\operatorname{Var}(X)=10$ and $\operatorname{Var}(Y)=20$. Regressing $y$ on $x$ by OLS (with intercept) gives slope $1$. What slope do you get when you instead regress $x$ on $y$ (with intercept)? Answer $-100$ if it cannot be determined.

$1/2$. Both slopes share the covariance: $\beta_{y|x}=\operatorname{Cov}/\operatorname{Var}(X)$ and $\beta_{x|y}=\operatorname{Cov}/\operatorname{Var}(Y)$. So $\beta_{x|y}=\beta_{y|x}\cdot\tfrac{10}{20}=\tfrac12$.