# Parallel and Perpendicular Lines

Parallel lines are coplanar lines that never intersect.

In two dimensions, parallel lines have the same slope .

**
Example:
**

The two lines

$\begin{array}{l}y=3x+8\\ y=3x-4\end{array}$

are parallel, since they both have slope $3$ .

**
Perpendicular lines
**
are lines that intersect at right angles. If you multiply the slopes of two perpendicular lines, you get
$-1$
.

**
Example:
**

The lines

$\begin{array}{l}y=-\frac{1}{3}x+2\\ y=3x-4\end{array}$

are perpendicular, since

$\left(-\frac{1}{3}\right)\left(3\right)=-1$

**
Exception
**
:
A horizontal line and a vertical line are perpendicular, even though the product of their slopes
$\left(0\times \infty \right)$
is undefined.