I was challenged with this question: Explain why the formula for determining slope using the coordinated of two points does not apply to vertical lines.

Question

This was my answer: The formula for determining a slope using two points does not apply to vertical lines simply because it would be illogical to divide by 0. To find a slope of a horizontal line we use the formulam= y1-y2/x1-x2 this stipulates that we have two points to work with.
Vertical lines have no slope. Thus, the concept of slope simply does not work for vertical lines. A vertical line will have no slope, and the slope is undefined.
A slope of 0=horizontal,
Vertical lines are in the form of x=some number, such as x=6; When a line involves an undefined slope the line is vertical, and when a line is vertical you will end up dividing by 0 if you try and compute slope.
According to page 530 of the text” a two point on a vertical line have the same x coordinate, thus the change in x is always 0, always undefined. The formula for

Answer 1

You have some errors:
"would be illogical" should be it is not defined (not allowed) to divide by zero.

Vertical slopes have no slope. Should be vertical lines have undefined slope.

Answer 2

find an equation of the line containing the given pair of points (-5,-7) & (-3,-8)