Question

How do you find the slope of a line perpendicular to a slope 0?

Answer 1

It will of the type `x=k`.

Explanation:

This appears to be a bit complicated as normally we say that if slope of a line is `m`, slope of line perpendicular to it is `-1/m`, which means just take the reciprocal and change the sign.

For example if slope of a line is `3/7`, line perpendicular to it will have a slope of `-7/3`. And if slope of a line is `-2`, slope of line perpendicular to it will be `1/2`.

What do we do if we have to find the slope of a line perpendicular to a line of slope `0`? The problem is `1/0` is not defined.

Way out is even simpler. As equation of a line whose slope is `0` is of the type `y=k_1` (here `k_1` a constant is `y`-intercept - aline parallel to `x`-axis),

equation of line perpendicular to it will be `x=k`, where `k` is another constant. Note `k` is `x`-intercept of the line `x=k` and this line is vertical i.e. parallel to `y`-axis.

Answer 2

The slope of a line perpendicular to a line with a slope of `0` is undefined. The perpendicular line is a vertical line.

Explanation:

The slope of a line perpendicular to a line with a slope of `0` is undefined. The perpendicular line is a vertical line.

A line with a slope of `0` is a horizontal line. A vertical line would be perpendicular to the horizontal line, but the slope of a vertical line is undefined.

For example:

The following points will result in a vertical line because the x-coordinates are the same.

`(2,3)` and `(2,4)`

`m=(4-3)/(2-2)`

`m=1/0`, which is undefined.

The points represent a vertical line with an undefined slope.

Answer 3

You cannot find the slope.
You can only say that it will be a vertical line and the slope is undefined.

Explanation:

A line with a slope of `0` is a horizontal line.

A line which is perpendicular to a horizontal line is a vertical line.

However, the slope of a vertical line is undefined.

So you cannot find the slope. You can only say that it will be a vertical line and the slope is undefined.

This is because for any change in `y` values, there is no change in the `x` values.

Slope = `(Delta y)/(Delta x) = y/0`