# How do you find the slope given x + 2y=3?

Jan 14, 2017

Convert the equation to the slope-intercept form - see entire explanation below:

#### Explanation:

To find the slope we need to convert the equation to the slope-intercept form by solving for $y$:

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 color(blue)(b is the y-intercept value.

$x + 2 y = 3$

$x + 2 y - \textcolor{red}{x} = - \textcolor{red}{x} + 3$

$x - \textcolor{red}{x} + 2 y = - \textcolor{red}{x} + 3$

$0 + 2 y = - x + 3$

$2 y = - x + 3$

$\frac{2 y}{\textcolor{red}{2}} = \frac{- x + 3}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} y}{\cancel{\textcolor{red}{2}}} = - \frac{x}{2} + \frac{3}{2}$

$y = - \frac{1}{2} x + \frac{3}{2}$

With the equation now in slope intercept form we can see the slope is $\textcolor{red}{m = - \frac{1}{2}}$