Question

Why is the slope unidentified for vertical lines

Answer 1

Vertical lines have the same x coordinate and the formula for a slope is y2-y1 divided by x2-x1
Let's just say , for example, that the x value is 7.
7-7=0
So, if the x values are the same, the denominator of the fraction becomes zero.
And, mathematically speaking, a fraction with a denominator of zero doesn't exist.

Answer 2

see below

Explanation:

Vertical lines have the same x coordinates

The slope is given by

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

The x values are the same

m = (y2-y1)/(x-x)

m = (y2-y1)/ 0

Any number, except 0, divided by 0 is undefined