Question

What is the equation of the line that passes through `(-4,1)` and is perpendicular to the line that passes through the following points: `(3,-3,),(1,-4)`?

Answer 1

`y = -2x - 7`

Explanation:

First, get the slope `m'` of the line that the line in question is perpendicular to.

`m' = (y_1 - y_2) / (x_1 - x_2)`

`=> m' = (-4 - -3) / (1 - 3)`

`=> m' = -1/-2 = 1/2`

Next, to get the slope `m` of the desired line, we get the negative reciprocal of the slope `m'` of the line is the perpendicular with

`m = -1/(m')`

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

Now that we have the slope `m` of the desired line, we must get the `y`-intercept of the line. We do this by substituting the coordinates of the point where we know the line passes through

`y = mx + b`
`=> y = -2x + b`

`=> 1 = -2(-4) + b`

`=> 1 = 8 + b`
`=> b = -7`

Hence, the equation of the line is

`y = -2x - 7`