Question

What is the slope of the line x = 4?

Answer 1

Undefined

Explanation:

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

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

In the case of the line `x=4`, which passes through the points `(4, 0)` and `(4, 1)`, the slope is given by:

`m = (1 - 0)/(4-4) = 1/0`

... which is undefined.

You might try to say that its slope is 'infinite', but actually it's not clear whether that should be `+oo` or `-oo`. It's better to recognise that division by `0` is undefined.