Question

When the line is horizontal, does the slope equal 0, or is it undefined?

Answer 1

The slope of a horizontal line is `0`.

Explanation:

On a horizontal line, all points have the same `y`-value, so the change in y over the change in x (the rise over the run) is always `0` over that change in `x`.

If we pick two different points on the line, they must have different `x` -values so we get `0` over a non-`0` number, which is `0`.

Example:

Line `y=3`,

points: `(1,3)`, `(5,3)` , then `m = (3-3)/(5-1) = 0/4 =0`

points: `(7,3)`, `(2,3)` , then `m = (3-3)/(2-7) = 0/(-5) =0`

points: `(a,3)`, `(b,3)` with `a != b`, then `m = (3-3)/(b-a) = 0/"non-0"=0`