Answer
$$ m_1m_2=-1 \Rightarrow m_1=\frac{-1}{m_2}$$
Work Step by Step
If the lines are perpendicular, then the angle between them is $\theta=\pi / 2 $
\begin{align*}
\cot (\pi / 2)&=\frac{1+m_{1} m_{2}}{m_{1}-m_{2}}
\\
0&=\frac{1+m_{1} m_{2}}{m_{1}-m_{2}}
\end{align*}
Then
$$ m_1m_2=-1 \Rightarrow m_1=\frac{-1}{m_2}$$
