# What is the slope of the line through the points (5, 2) and (5, -3)?

The slope of a line passing from two points $A \left({x}_{a} , {y}_{a}\right)$ and $B \left({x}_{b} , {y}_{b}\right)$ is:
$m = \frac{\Delta y}{\Delta x} = \frac{{y}_{a} - {y}_{b}}{{x}_{a} - {x}_{b}}$,
but in this case we can notice that ${x}_{a} = {x}_{b}$ so the line is vertical, so there is not defined the slope, or, better, the slope is infinite.