Question

How do you write an equation of a line perpendicular to y= 3/4x - 2 and passes through (-12,7)?

Answer 1

`y = -4/3x -9`

Explanation:

First we need to get the slope of the perpendicular line

The slope of a perpendicular line is equal to the negative inverse of the slope of the given line

`y = mx + b`

`y = 3/4x - 2`

`=> m = 3/4`

`m' = -1/m`

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

`=> m' = -4/3`

Now that we have the slope, we need to find the y-intercept.
To find the y-intercept, we need to plug-in values of `x` and `y` that the line passes through

`y' = m'x' + b`

`=> y' = -4/3x' + b`

`=> 7 = -4/3(-12) + b`

`=> 7 = 16 + b`

`=> b = -9`

Therefore, the equation of the line is

`y = -4/3x -9`