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

Oct 8, 2017

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: $y = 0$

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

$3 x + 0 = 6$

$3 x = 6$

3x/color(red)(3) = 6/colorred)(3)

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

We can now 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)^2-0.125)((x-2)^2+ y^2-0.125)(3x+2y-6)=0 [-20, 20, -10, 10]}

Now, we can shade the left side of the line. And we need to make the boundary line a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(3x+2y-6) < 0 [-20, 20, -10, 10]}