Question

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

Answer 1

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?

`(y2 - y1)/(x2 - x1)`

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 - (-5),` 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.