# Is the slope of x = 0 is undefined?

Jun 21, 2015

Yes, the slope of the line given by the equation $x = 0$ is undefined.

#### Explanation:

If a line passes through two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ then the slope $m$ of the line is given by the formula:

$m = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

In our case, then line $x = 0$ passes through $\left(0 , 0\right)$ and $\left(0 , 1\right)$, so we can (attempt to) calculate its slope as:

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{1 - 0}{0 - 0} = \frac{1}{0}$

$\frac{1}{0}$ is undefined, so the slope is undefined.