Question

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

Answer 1

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.

Answer 2

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).