# How do you graph the inequality 2x+y< -3?

Aug 16, 2017

See a solution process below:

#### Explanation:

First calculate two points on the line for this as an equation instead of an inequality to find the border of the inequality:

For $x = 0$: $\left(2 \times 0\right) + y = - 3$

$0 + y = - 3$

$y = - 3$ or $\left(0 , - 3\right)$

For $x = - 3$: $\left(2 \times - 3\right) + y = - 3$

$- 6 + y = - 3$

$\textcolor{red}{6} - 6 + y = \textcolor{red}{6} - 3$

$0 + y = 3$

$y = 3$ or $\left(- 3 , 3\right)$

We can now plot these two points and draw a line through them to find the border of the inequality:

graph{(x^2+(y+3)^2-0.05)((x+3)^2+(y-3)^2-0.05)(2x+y+3)=0}

Now that we have the border we can chart the inequality. Because the inequality operator contains a "or equal to" clause it will stay as a solid line. And because it has a "less than" clause we will shade to the left of the line:

graph{(2x+y+3)<=0}