Question

How do I change an Ax+By=C equation to a y=mx+b equation where m is the slope and b is the y intercept like 4x+2y=8?

Answer 1

`y=(-A/B)x+C/A`

Explanation:

If
`color(white)("XXX")Ax+By=C`
then
after subtracting `Ax` from both sides:
`color(white)("XXX")By=-Ax+C`
then dividing both sides by `B`
`color(white)("XXX")y=(-A/B)x+C/A`
which is the slope-intercept form with
`color(white)("XXX")`slope`=(-A/B)`
and
`color(white)("XXX")`y-intercept`=(C/A)`

Answer 2

`y=-2x+4`

Explanation:

`"Rearrange "4x+2y=8" into required form"`

`"subtract "4x" from both sides"`

`cancel(4x)cancel(-4x)+2y=-4x+8`

`rArr2y=-4x+8`

`"divide all terms by 2"`

`(cancel(2) y)/cancel(2)=(-4)/2x+8/2`

`rArry=-2x+4larrcolor(red)"in slope-intercept form"`