Why does the slope formula not work on vertical lines?

The slope formula is defined as the rise over the run, a.k.a the change in Y over the change in X.

m= (y1-y2)/(x1-x2).

For a Vertical Line, the rise is infinite while the run is zero, suggesting a slope of infinity/zero (because the slope is the rise over the run).

Zero can be put into infinity an infinite amount of times, describing an INFINITE SLOPE, which limit calculus is required to reveal. However, for algebra students, this value, infinity, or the infinite slope, is described as UNDEFINED. This is because algebra students have not yet received sufficient math tools to define infinity! Be patient and don't get too excited, calculus will reveal much :)

SO...

For CALCULUS students: Vertical lines have an infinite slope

For ALGEBRA students: Vertical lines have an undefined slope