# How do you find the slope of a line perpendicular to a slope 0?

May 9, 2018

It will of the type $x = k$.

#### Explanation:

This appears to be a bit complicated as normally we say that if slope of a line is $m$, slope of line perpendicular to it is $- \frac{1}{m}$, which means just take the reciprocal and change the sign.

For example if slope of a line is $\frac{3}{7}$, line perpendicular to it will have a slope of $- \frac{7}{3}$. And if slope of a line is $- 2$, slope of line perpendicular to it will be $\frac{1}{2}$.

What do we do if we have to find the slope of a line perpendicular to a line of slope $0$? The problem is $\frac{1}{0}$ is not defined.

Way out is even simpler. As equation of a line whose slope is $0$ is of the type $y = {k}_{1}$ (here ${k}_{1}$ a constant is $y$-intercept - aline parallel to $x$-axis),

equation of line perpendicular to it will be $x = k$, where $k$ is another constant. Note $k$ is $x$-intercept of the line $x = k$ and this line is vertical i.e. parallel to $y$-axis.

May 9, 2018

The slope of a line perpendicular to a line with a slope of $0$ is undefined. The perpendicular line is a vertical line.

#### Explanation:

The slope of a line perpendicular to a line with a slope of $0$ is undefined. The perpendicular line is a vertical line.

A line with a slope of $0$ is a horizontal line. A vertical line would be perpendicular to the horizontal line, but the slope of a vertical line is undefined.

For example:

The following points will result in a vertical line because the x-coordinates are the same.

$\left(2 , 3\right)$ and $\left(2 , 4\right)$

$m = \frac{4 - 3}{2 - 2}$

$m = \frac{1}{0}$, which is undefined.

The points represent a vertical line with an undefined slope. May 9, 2018

You cannot find the slope.
You can only say that it will be a vertical line and the slope is undefined.

#### Explanation:

A line with a slope of $0$ is a horizontal line.

A line which is perpendicular to a horizontal line is a vertical line.

However, the slope of a vertical line is undefined.

So you cannot find the slope. You can only say that it will be a vertical line and the slope is undefined.

This is because for any change in $y$ values, there is no change in the $x$ values.

Slope = $\frac{\Delta y}{\Delta x} = \frac{y}{0}$