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

1 Answer
Jul 19, 2015

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.