# How do you write the slope intercept form of the line 6x+5y=-15?

Jan 27, 2017

$y = \textcolor{red}{- \frac{6}{5}} x - \textcolor{b l u e}{3}$

#### 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.

We need to solve this equation for $y$:

$6 x + 5 y = - 15$

$6 x - \textcolor{red}{6 x} + 5 y = - \textcolor{red}{6 x} - 15$

$0 + 5 y = - 6 x - 15$

$5 y = - 6 x - 15$

$\frac{5 y}{\textcolor{red}{5}} = \frac{- 6 x - 15}{\textcolor{red}{5}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} y}{\cancel{\textcolor{red}{5}}} = \frac{- 6 x}{5} - \frac{15}{5}$

$y = - \frac{6}{5} x - 3$