# What is the slope of the line x = 4?

Nov 11, 2015

Undefined

#### Explanation:

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

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

In the case of the line $x = 4$, which passes through the points $\left(4 , 0\right)$ and $\left(4 , 1\right)$, the slope is given by:

$m = \frac{1 - 0}{4 - 4} = \frac{1}{0}$

... which is undefined.

You might try to say that its slope is 'infinite', but actually it's not clear whether that should be $+ \infty$ or $- \infty$. It's better to recognise that division by $0$ is undefined.