Question

Is the slope of x = 0 is undefined?

Answer 1

Yes, the slope of the line given by the equation `x=0` is undefined.

Explanation:

If a line passes through two points `(x_1, y_1)` and `(x_2, y_2)` then the slope `m` of the line is given by the formula:

`m = (Delta y)/(Delta x) = (y_2 - y_1)/(x_2 - x_1)`

In our case, then line `x=0` passes through `(0, 0)` and `(0, 1)`, so we can (attempt to) calculate its slope as:

`m = (y_2 - y_1)/(x_2 - x_1) = (1 - 0) / (0 - 0) = 1/0`

`1/0` is undefined, so the slope is undefined.