- Parallel
For two straight lines $\ell_1$ and $\ell_2$ with slopes $m_1$ and $m_2$ respectively.
\begin{equation*}
\mbox{If } \ell_1 // \ell_2\mbox{, then } m_1= m_2,
\end{equation*}
and vice versa. - Perpendicular
For two straight lines $\ell_1$ and $\ell_2$ with slopes $m_1$ and $m_2$ respectively.
\begin{equation*}
\mbox{If } \ell_1 \perp \ell_2 \mbox{, then } m_1\times m_2 = -1,
\end{equation*}
and vice versa.