# How do you find the slope for x=1?

Feb 4, 2017

Its slope is undefined.

#### Explanation:

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

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

The given equation $x = 1$ describes a vertical line passing through all points of the form $\left(1 , y\right)$, including $\left({x}_{1} , {y}_{1}\right) = \left(1 , 0\right)$ and $\left({x}_{2} , {y}_{2}\right) = \left(1 , 1\right)$.

So its slope is given by the formula:

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

which is undefined.