# What is the slope-intercept form of this equation 3x + 9y = 18?

Mar 21, 2017

See the entire solution process below:

#### Explanation:

The slope-intercept form of a linear equation is: $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept value.

Therefore we must solve this equation for $y$:

$3 x + 9 y = 18$

$- \textcolor{red}{3 x} + 3 x + 9 y = - \textcolor{red}{3 x} + 18$

$0 + 9 y = - 3 x + 18$

$9 y = - 3 x + 18$

$\frac{9 y}{\textcolor{red}{9}} = \frac{- 3 x + 18}{\textcolor{red}{9}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{9}}} y}{\cancel{\textcolor{red}{9}}} = \frac{- 3 x}{\textcolor{red}{9}} + \frac{18}{\textcolor{red}{9}}$

$y = \textcolor{red}{- \frac{1}{3}} x + \textcolor{b l u e}{2}$