Question

How do you find the slope and intercept of `-4x+2y=12`?

Answer 1

Slope: `2`
y-intercept: `6`
(x-intercept: `-3`)

Explanation:

slope
Given an equation in the form `Ax+By=C` the slope is `(-A/B)`
So `-4x+2y=12` has a slope of `-(-4)/2=2`

Alternately, we could convert the given form
into "slope-intercept form": `y=mx+b` with slope `m` and y-intercept `b`
`color(white)("XXX")-4x+2y=12`
`color(white)("XXX")rarr 2y=4x+12`
`color(white)("XXX")rarr y = 2x+6`

y-intercept
If we used the "slope-intercept form" (above) we already have the y-intercept: `6`;
otherwise we can determine the y-intercept by finding the value of `y` when `x=0` in the given equation: `-4x+2y=12`
`color(white)("XXX")-4xx(0)+2y=12`
`color(white)("XXX")rarr y=6`

x-intercept (note sometimes when "the intercept" is asked for, what is meant is only the y-intercept)
The x-intercept can be determined by find the value of `x` when `y=0` in the given equation: `-4x+2y=12`
`color(white)("XXX")-4x+2xx(0)=12`
`color(white)("XXX")rarr x=-3`