Question

If line `q` has a slope of -2, what is the slope of any line perpendicular to `q`?

Answer 1

The slope of any line perpendicular to `q` will be `1/2`.

Explanation:

The slopes of perpendicular lines will be opposite reciprocals of each other.

In the phrase "opposite reciprocals," the word "opposite" means negative, and "reciprocal" means a flipped fraction. To achieve the opposite reciprocal of a number, simply flip it, then multiply by `-1`.

For example, the opposite reciprocal of `1/3`:

`1/3=>3/1*-1=3*-1=-3`

If the number doesn't happen to be a fraction and you can't flip it, simply add a `1` under it to represent division by `1` (which doesn't change the number). For instance, the opposite reciprocal of `2`:

`2=2/1=>1/2*-1=-1/2`

In this problem, we want the opposite reciprocal of `-2`, which is:

`-2=(-2)/1=>1/(-2)*-1=(-1)/(-2)=1/2`

That means the slope of any line perpendicular to line `q` will have a slope of `1/2`.

Answer 2

`1/2`

Explanation:

`"given a line with slope m then the slope of any line"`
`"perpendicular to it is"`

`•color(white)(x)m_(color(red)"perpendicular")=-1/m`

`"here "m=-2`

`rArrm_(color(red)"perpendicular")=-1/(-2)=1/2`