Question

What is the slope of `x=6` ?

Answer 1

The slope of a vertical line is undefined.

Explanation:

Given:

`x=6`

This equation describes a vertical line.

The slope of a line describes how much it rises in proportion to its run.

Given two distinct points `(x_1, y_1)` and `(x_2, y_2)`, the slope `m` of the line through them is given by the formula:

`m = ("change in " y)/("change in " x) = (y_2-y_1)/(x_2-x_1)`

In our example, consider the two distinct points `(6, 0)` and `(6, 1)`.

Both of these satisfy the equation `x=6`, so lie on the line.

So the slope of the line is:

`m = (1 - 0)/(6 - 6) = 1/0`

which is undefined, since division by `0` is (almost) always undefined.

graph{(x+y*0.000001-6)((x-6)^2+y^2-0.006)((x-6)^2+(y-1)^2-0.006)=0 [-0.73, 9.27, -1.94, 3.06]}