# How do you graph the inequality 2y - 3x >6?

May 27, 2017

Draw the line then shade where it is true. See below.

#### Explanation:

Strategy: Figure out what the line would look like using $2 y - 3 x = 6$. Then, plugging in a few choice points, find $x$ and $y$ values that, when plugged in, are truly greater than $6$. Shade the side where the inequality is true.

Step 1. Graph the line $2 y - 3 x = 6$

Rewrite this equation with $y$ on one side alone.
$2 y = 3 x + 6$
$y = \frac{3}{2} x + 3$

Slope: $m = \frac{3}{2}$, that is a rise of 3 and run of 2
$y$-intercept: $\left(0 , 3\right)$

graph{y=3/2x+3}

Step 2. Find some points where $x$ and $y$ will make the inequality true.

Try the point $\left(0 , 0\right)$:
$2 \left(0\right) - 3 \left(0\right) > 6$ or $0 > 6$ is FALSE. Do not shade this side of the line.

Try the point $\left(- 5 , 0\right)$:
$2 \left(0\right) - 3 \left(- 5\right) > 6$ or $15 > 6$ is TRUE. So, do shade this side of the line.

Because the inequality is $>$, use a dashed line.

graph{2y-3x>6}