Why does the slope of a vertical line not exist? Can you provide a geometric interpretation?

Vertical lines have an undefined slope because the horizontal change is 0 — you cannot divide a number by 0. The slope of a line is a measure of its steepness. Vertical lines have NO SLOPE.

Vertical lines cross the x-axis where y = 0. Can this also be a reason why vertical lines have no slope? I understand the steepness explanation.