# How do you graph 3x + 2y<6?

Jun 3, 2018

See a solution process below:

#### Explanation:

First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.

For: $x = 0$

$\left(3 \cdot 0\right) + 2 y = 6$

$0 + 2 y = 6$

$2 y = 6$

$\frac{2 y}{\textcolor{red}{2}} = \frac{6}{\textcolor{red}{2}}$

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

For: $x = 2$

$\left(3 \cdot 2\right) + 2 y = 6$

$6 + 2 y = 6$

$- \textcolor{red}{6} + 6 + 2 y = - \textcolor{red}{6} + 6$

$0 + 2 y = 0$

$2 y = 0$

$\frac{2 y}{\textcolor{red}{2}} = \frac{0}{\textcolor{red}{2}}$

$y = 0$ or $\left(2 , 0\right)$

We can then graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.

graph{(x^2+(y-3)^2-0.035)((x-2)^2+y^2-0.035)(3x+2y-6)=0 [-10, 10, -5, 5]}

Now, we can shade the left side of the line.

We also need to change the boundary line to a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(3x+2y-6) < 0 [-10, 10, -5, 5]}