What is the slope of a line that is parallel to a vertical line?

2 Answers
George C.
Jul 22, 2015

Any line that is parallel to a vertical line is also vertical and has undefined slope.

Explanation:

A vertical line is given by the equation x = ax=a for some constant aa. This line passes through the points (a, 0)(a,0) and (a, 1)(a,1).

Its slope mm is given by the formula:

m = (Delta y) / (Delta x) = (y_2 - y_1) / (x_2 - x_1) = (1 - 0) / (a - a) = 1/0

which is undefined.

Alan P.
Jul 22, 2015

A vertical line and all lines parallel to it have undefined slopes

Explanation:

Note that if a line is vertical, all lines parallel to it are also vertical.

For any two points (x_1,y_1) and (x_2, y_2) on a line
the slope is defined as (y_2-y_1)/(x_2-x_1)

BUT if the line is vertical x_1 = x_2 for all points on the line
and therefore the definition of the slope would require dividing by zero (which is undefined).

Related questions
See all questions in Horizontal and Vertical Line Graphs
Impact of this question
5121 views around the world
You can reuse this answer
Creative Commons License