Question

What is `3x-4y=12` in slope-intercept form?

Answer 1

`y = 3/4x-3`

Explanation:

Slope-intercept form means we are looking for an equation of the type `y = mx+b`

Starting with `3x-4y=12`, we can add `4y` to each side, yielding
`3x-4y+4y=12+4y`
and `-4y+4y = 0`, so we are left with
`3x=12+4y`
We now subtract 12 from both sides:
`3x-12=12+4y-12`
`12-12 = 0`, leaving us with:
`3x-12 = 4y`
We now divide by 4 on both sides:
`(3x-12)/4 = (4y)/4`
We know `(4y)/4 = y`
On the left hand side, we can split `(3x-12)/4` into `(3x)/4 - 12/4`.
Simplifying, we find `3/4x - 3 = y`, which is in slope intercept form, as requested.