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

1 Answer
George C.
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.

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