Answer
A vertical line has an undefined slope because of the way the slope formula is written.
The slope formula is:
slope = $\frac{y_{final} - y_{initial}}{x_{final} - x_{initial}}$
A vertical line has the same x value for any y value, so between any two points on the line, the change in x will be zero. This means the slope would be:
slope = $\frac{y_{final} - y_{initial}}{0}$
Since it is not mathematically possible to divide by 0, the slope is undefined.
Work Step by Step
A vertical line has an undefined slope because of the way the slope formula is written.
The slope formula is:
slope = $\frac{y_{final} - y_{initial}}{x_{final} - x_{initial}}$
A vertical line has the same x value for any y value, so between any two points on the line, the change in x will be zero. This means the slope would be:
slope = $\frac{y_{final} - y_{initial}}{0}$
Since it is not mathematically possible to divide by 0, the slope is undefined.
