Answer
If two lines are perpendicular, then their slopes are negative reciprocals of each other.
Work Step by Step
If two lines are perpendicular, then their slopes are negative reciprocals of each other.
For example:
Let $y=3x+3\text{ and }y=-\frac{1}{3}x+3$ be the equations of two non-vertical lines with the slope $3\text{ and}-\frac{1}{3}$respectively.
The product of the slopes is given as
$\begin{align}
& {{m}_{1}}{{m}_{2}}=3\left( -\frac{1}{3} \right) \\
& =-1
\end{align}$
Thus, the product of their slopes is $-1$.
From the graph, one can conclude that both lines given by the equations $y=3x+3\text{ and }y=-\frac{1}{3}x+3$ are perpendicular.
Hence, if the lines are perpendicular, then the product of their slopes is $-1$.
Thus, the slopes of the two perpendicular lines are negative reciprocals of each other.
