Explain why the slope of a vertical line is called undefined

The slope of a line is: "the change in y" over "the change in x";

or: "rise over run". A vertical line has NO "change in y" over "change in x"; that is, has NO "rise over run"; so there is NO particular slope to mention or define. As such, the slope of a vertical line is "undefined".

The slope of the line is undefined because when you use the slope formula (y2-y1) / (x2-x1) you end up dividing by zero.