# How do you graph 3x - 2y ≥ 6?

Jul 1, 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: $y = 0$

$3 x - \left(2 \times 0\right) = 6$

$3 x - 0 = 6$

$3 x = 6$

$\frac{3 x}{\textcolor{red}{3}} = \frac{6}{\textcolor{red}{3}}$

$x = 2$ 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.
The boundary line will be solid because the inequality operator contains an "or equal to" clause.

graph{(x^2+(y+3)^2-0.04)((x-2)^2+y^2-0.04)(3x-2y-6)=0 [-10, 10, -5, 5]}

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

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