What is the slope of the line x = 4?

1 Answer
Nov 11, 2015

Answer:

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)#

In the case of the line #x=4#, which passes through the points #(4, 0)# and #(4, 1)#, the slope is given by:

#m = (1 - 0)/(4-4) = 1/0#

... which is undefined.

You might try to say that its slope is 'infinite', but actually it's not clear whether that should be #+oo# or #-oo#. It's better to recognise that division by #0# is undefined.