Question

The slope of a horizontal line is zero, but why is the slope of a vertical line undefined (not zero)?

Answer 1

It's like the difference between `0/1` and `1/0`.

`0/1 = 0` but `1/0` is undefined.

Explanation:

The slope `m` of a line passing through two points `(x_1, y_1)` and `(x_2, y_2)` is given by the formula:

`m = (Delta y) / (Delta x) = (y_2 - y_1) / (x_2 - x_1)`

If `y_1 = y_2` and `x_1 != x_2` then the line is horizontal: `Delta y = 0`, `Delta x != 0` and `m = 0 / (x_2 - x_1) = 0`

If `x_1 = x_2` and `y_1 != y_2` then the line is vertical: `Delta y != 0`, `Delta x = 0` and `m = (y_2 - y_1) / 0` is undefined.