# What is the slope of a line that is perpendicular to a slope of 0?

Jul 20, 2016

Undefined.

#### Explanation:

That is the only slope which cannot be defined by a number!

A line with a slope of zero is a horizontal line where, for any change in x, the change in y is always 0.

$m = \frac{0}{3} , \frac{0}{8} , \frac{0}{x}$ as long as x is not 0.

The line perpendicular to this is a vertical line which has a slope which is 'undefined'. For any change in y, the change in x is always 0, but we cannot divide by 0.

$m = \frac{6}{0} , \frac{- 5}{0} , \frac{y}{0}$ etc. The slope remains undefined!

Jul 20, 2016

A line that has a slope of $0$ has no rise and is therefore a horizontal line. The perpendicular line to this would be a vertical line whose slope is undefined as there would be $0$ run.
A slope of $0$ is a horizontal line with no rise. This line is represented as $y =$
An undefined slope is a vertical line with no run. This line is represented as $x =$