Example

The line $L$ passes through the points $(0,3)$ and $(-3,3)$. Find an equation of a line parallel to $L$. Find an equation of a line perpendicular to $L$.

Solution

The line $L$ is a horizontal line---the $y$-coordinates of the points on the line are the same. Furthermore, it's slope is 0:

An equation for line $L$ is $y=3$.

Any line parallel to $L$ must be another horizontal line, for example, $y=1$ or $y=-7$ or $y=2573$.

A line perpendicular to $L$ must be a vertical line. The $x$-coordinates of all points on a vertical line are the same. Every vertical line has an equation that can be written in the form $x=a$, for some fixed number $a$. For example, equations of vertical lines are $x=-9$, $x=10$, $x=17.35$, etc.