Question

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

Answer 1

Slope: `1/3`

Explanation:

Two ways to determine the slope for a question like this one.

Method 1: convert the given equation into slope-intercept form.
An equation in the form:
`color(white)("XXX")y=color(green)(m)x+color(blue)(b)`
is in "slope-intercept form" with a slope of `color(green)(m)` and a y-intercept of `color(blue)(b)`

Given
`color(white)("XXX")-x+3y=-12`

`color(white)("XXX")3y=x-12`

`color(white)("XXX")y=color(green)(1/3)x+color(blue)(""(-6))`

Method 2: less common for some reason
Given an equation in the form
`color(white)("XXX")Ax+By=C`
the slope is `color(red)(-A/B)`

For the given example
`color(white)("XXX")A=(-1)color(white)("XX")andcolor(white)("XX")B=3`