Question

Why is the slope of a vertical line “undefined”?

Short answer

Vertical lines have no slope. We can't divide by zero, which is why this slope value is "undefined"

Step-by-step solution

. Given Information

We are given a vertical line in a graph and we know that it's slope is undefined

. Slope formula

To find a slope we use the formula :

$\frac{y_2-y_1}{x_2-x_1}$

. Reason for the slope to be undefined 

In a vertical line the different in x-axis is zero and in the formula for slope we see the x-axis is in denominator and anything divided by zero gives us undefined , so

Vertical lines have no slope. We can't divide by zero, which is why this slope value is "undefined"