Let two straight lines of the $xy$-plane have the slopes $m_{1}$ and $m_{2}$.  The lines are at right angles to each other iff $m_{1}$ and $m_{2}$ are the opposite inverses of each other, i.e. iff

Example.  The lines  $y=(1+\sqrt{2})x$  and  $y=(1-\sqrt{2})x$  are at right angles to each other.