# How do you find the slope perpendicular to x = 0?

Nov 6, 2015

0

#### Explanation:

Compare to:

The slope for $x = 2$ is a vertical line perpendicular to the x-axis but crossing the x-axis at $x = 2$

So the slope $x = 0$ is vertical to the axis but crossing it at $x = 0$. In other words it is the y-axis.

Slope (gradient) is the amount of up for the amount of along

$\to \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

The slope for $x = 0$ can not be quantitised as you are unable to have different values for x_1 "and x_2. In fact the only truth is that ${x}_{1} = {x}_{2}$ so you would have $\frac{{y}_{2} - {y}_{1}}{0}$ which is undefined!

The perpendicular to the y-axis is parallel to the x-axis. In this case ${y}_{1} = {y}_{2} \to \frac{0}{{x}_{2} - {x}_{1}} = 0$ which is defined.

So the slope (gradient) perpendicular to $x = 0$ is 0.

There is no up for any amount of along!