Why is the slope unidentified for vertical lines

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.

see below

Step-by-step 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