smc

By the Triangle Inequality, $PR+QR\ge PR$, and equality holds if $R$ is on $PQ$. The equation of the line with $P$ and $Q$ is $y=\frac{4}{5}x-\frac{6}{5}$, so point $R$ is $(1,-\frac{2}{5})$. Thus, $m=\boxed{-\frac{2}{5}}$.