Would x = 5 be an undefined slope?

Jun 13, 2015

The line described by the equation $x = 5$ has undefined slope.

Explanation:

If a line passes through points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ then its slope 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 $x = 5$ choose example points $\left(5 , 0\right)$ and $\left(5 , 1\right)$.

Then $m = \frac{1 - 0}{5 - 5} = \frac{1}{0}$ which is undefined.