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

Aug 8, 2015

The slope of $2 x + y = 3$ is $- 2$

#### Explanation:

Method 1
For a linear equation in standard form
$\textcolor{w h i t e}{\text{XXXX}}$$A x + B y = C$
the slope is given by the equation
$\textcolor{w h i t e}{\text{XXXX}}$$m = - \frac{A}{B}$

In this case that becomes
$\textcolor{w h i t e}{\text{XXXX}}$$m = - \frac{2}{1} = - 2$

Method 2 (more common, but often more work)
Convert the equation into "slope-point form":
$\textcolor{w h i t e}{\text{XXXX}}$$y = m x + b$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$with a slope of $m$ and a y-intercept of $b$

$2 x + y = 3$

$\rightarrow$$\textcolor{w h i t e}{\text{XXXX}}$$y = - 2 x + 3$