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

May 25, 2016

Slope: $\frac{1}{3}$

#### 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:
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{g r e e n}{m} x + \textcolor{b l u e}{b}$
is in "slope-intercept form" with a slope of $\textcolor{g r e e n}{m}$ and a y-intercept of $\textcolor{b l u e}{b}$

Given
$\textcolor{w h i t e}{\text{XXX}} - x + 3 y = - 12$

$\textcolor{w h i t e}{\text{XXX}} 3 y = x - 12$

$\textcolor{w h i t e}{\text{XXX")y=color(green)(1/3)x+color(blue)(} \left(- 6\right)}$

Method 2: less common for some reason
Given an equation in the form
$\textcolor{w h i t e}{\text{XXX}} A x + B y = C$
the slope is $\textcolor{red}{- \frac{A}{B}}$

For the given example
$\textcolor{w h i t e}{\text{XXX")A=(-1)color(white)("XX")andcolor(white)("XX}} B = 3$