Question

How do you find the slope and y intercept of `-12x+3y=-60`?

Answer 1

Slope: `4`
y-intercept: `-20`

Explanation:

Method 1
For a linear equation in standard form: `Ax+By=C`
`color(white)("XXX")`the slope is `m=-A/B`
In this case `A=-12` and `B=3`
`color(white)("XXX")`so the slope is `m=-(-12)/3 = 4`

The y-intercept is the value of `y` when `x=0`
Replacing `x` with `0` in the original equation:
`color(white)("XXX")-12(0)+3y =-60`
`rarrcolor(white)("XXX")3=-20`

Method 2
Alternately, you could rearrange the expression into "slope-intercept form: `y=mx+b`
(with slope `=m` and y-intercept `=b`)

Given
`color(white)("XXX")-12x+3y=-160`
Add `12x` to both sides
`color(white)("XXX")3y= 12x-60`
Divide by `3`
`color(white)("XXX")y=4x-20`
`color(white)("XXXXX") (=4x+(-20))`
which is "slope-intercept form"
with slope `m=4` and y-intercept`=-20`