someone explain to me how to find the slope if it exists and you only know x

Question

for example what is the slope of x=-8

Answer 1

If you graph X=8  you get a straight line where X is ALWAYS 8.

In other words it is a vertical line that crosses the X axis at X=8.

 

A flat or horizontal line has slope = 0.

A vertical line has a slope of ΔY/ΔX  and ΔX = 0

so the slope is ΔY/0  and division is undefined.

 

But every line that is close to vertical does have a slope and as

the line gets more and more vertical and closer and closer to vertical

the slope get larger and larger and larger and gets closer and closer to infinity.

So the slope approaches or has a limit of infinity - but mathematically is undefined.