# How do you find the intercepts for 2x+y=6?

Nov 6, 2016

The $x$ intercept is $\left(3 , 0\right)$ and the $y$ intercept is $\left(0 , 6\right)$.

#### Explanation:

$2 \textcolor{b l u e}{x} + \textcolor{red}{y} = 6$

The $x$ intercept is the point where the line crosses the $x$ axis.
$y = 0$ everywhere on the $x$ axis.

To find the $x$ intercept, substitute $\textcolor{red}{y} = \textcolor{red}{0}$ into the equation and solve for $\textcolor{b l u e}{x}$.

$2 \textcolor{b l u e}{x} + \textcolor{red}{0} = 6$

$2 \textcolor{b l u e}{x} = 6$

$\frac{2 \textcolor{b l u e}{x}}{2} = \frac{6}{2} \textcolor{w h i t e}{a a a}$Divide both sides by 2

$\textcolor{b l u e}{x} = 3$

The $x$ intercept is then $\left(3 , 0\right)$.

The $y$ intercept is the point where the line crosses the $y$ axis.
$x = 0$ everywhere on the $y$ axis.

To find the $y$ intercept, substitute $\textcolor{b l u e}{x} = \textcolor{b l u e}{0}$ into the equation and solve for $\textcolor{red}{y}$.

$2 \left(\textcolor{b l u e}{0}\right) + \textcolor{red}{y} = 6$

$\textcolor{red}{y} = 6$.

The $y$ intercept is then $\left(0 , 6\right)$.