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 = a# for some constant #a#. This line passes through the points #(a, 0)# and #(a, 1)#.

Its slope #m# 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).

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