Question

What is an equation of the line that passes through the point (-9,5) and is perpendicular to the line whose equation is `y=1/2x+5`?

Answer 1

`y = -2x - 13`

Explanation:

Perpendicular lines `L` and `L'` with slopes `m` and `m'`, respectively, have the following property with the slopes

`m = -1/m`

In case the slope is 0, the slope of the perpendicular line would be undefined, and vice versa. This would mean you are dealing with horizontal/vertical lines.

Given the line `L: y = 1/2x + 5`, we have

`m = 1/2`

Which means the line `L'` which is perpendicular to `L` has the following slope

`m' = -1/(1/2)`

`=> m' = -2`

---

Now that we know the slope of `L'`, let's find its y-intercept.

`L': y = -2x + b`

To find the y-intercept, let's insert the point which we know lies on the line `L'`.

`p': (-9, 5)`

`=> L': 5 = -2(-9) + b`

`=> -13 = b`

Therefore, the equation of the line `L'` which is perpendicular to `L` and passes through the point `(-9, 5)` is

`y = -2x - 13`