# What is the slope and y-intercept of the line x = -5?

Aug 26, 2016

This equation is a vertical line.

#### Explanation:

Which means that, regardless of the value of y, x is always $- 5$.

It has no y-intercept because it never crosses the y-axis.
It just goes up and down (theoretically forever) at the x-value of $- 5$.

This equation also has an undefined slope. Slope is the Rise over the Run, right?

$\frac{y 2 - y 1}{x 2 - x 1}$

Suppose y2 = 5 and y1 = 3. Then the Rise is 2 for every change in x-value.

But x doesn't change. For the Run, you can't choose two DIFFERENT values for x. X is always - 5.

If you subtract $- 5 - \left(- 5\right) ,$ you get zero, and division by zero is undefined.

A vertical line has an undefined slope.

So the equation $x = - 5$ has no defined slope and no y-intercept.