# How do you find the slope for (4,2) and (4,5)?

Sep 18, 2015

The line through $\left(4 , 2\right)$ and $\left(4 , 5\right)$ is vertical and as such has an undefined slope

#### Explanation:

For two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ the slope is given by

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

if $\left({x}_{2} - {x}_{1}\right) \ne 0$

but in this case $\left({x}_{2} - {x}_{1}\right) = \left(4 - 4\right) = 0$
and therefore the slope is undefined.