Question

How do you find the slope that is perpendicular to the line `y= -1`?

Answer 1

It is undefined.

Explanation:

The slope `m` of a line passing through 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)`

The line `y = -1` passes through the points `(0, -1)` and `(1, -1)`. So it has slope:

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

Alternatively, simply note that `y=-1` can be rewritten:

`y = 0x+(-1)`

which is in standard slope intercept form:

`y = mx+b`

with slope `m = 0` and intercept `b=-1`.

`color(white)()`
If a line has non-zero slope `m`, then any line perpendicular to it will have slope `-1/m`.

The line `y=-1` has slope `0` so any line perpendicular to it will have undefined slope. If you try to evaluate `-1/m`, it involves division by `0`, which has undefined result.