Question

How do you find the equation of the line in slope-intercept form that is perpendicular to the line -4x - 3y = 9 and passes through (12, -7)?

Answer 1

`y=3/4x-16`

Explanation:

`-4x-3y=9`
can be re-written in slope intercept form as:
`y = -4/3x-3`
and therefore has a slope of `(-4/3)`

Lines which are perpendicular to each other have slopes that are the negative reciprocal of one another.

Therefore any line perpendicular to `-4x-3y=9` has a slope of
`m= 3/4`

Since the desired line has a slope of `3/4` and passes through `(12,-7)` we can write it's equation in slope-point form as:
`(y-(-7)) = 3/4(x-12)`

Simplifying:
`y+7 = 3/4x-9`
or
`y=3/4x-16color(white)("XXXX")`which is slope-intercept form.