# How do I graph this inequality 3x+2y>5?

Apr 16, 2015

Start by isolating $y$ on the left side of the inequality

$3 x + 2 y > 5$

2y > -2x + 5 |:2

$y > - \frac{3}{2} x + \frac{5}{2}$

Now calculate the x and y-intercepts by making $y = 0$ (for the x-intercept), and then $x = 0$ (for the y-intercept).

These two points will allow you to draw the line

$y = - \frac{3}{2} x + \frac{5}{2}$

So,

$x = 0 \implies y = + \frac{5}{2}$

$y = 0 \implies 0 = - \frac{3}{2} x + 5 \implies x = \frac{5}{3}$

Here's how that line would look

graph{-3/2x + 5/2 [-10, 10, -5, 5]}

However, since your inequality requires that $y$ be greater than$- \frac{3}{2} x + \frac{5}{2}$, the solution region you're interested in must be above the line and not include the line.

You'll end up with a graph in which you have a dashed line and the shaded region above that line.

graph{y > -3/2x + 5/2 [-10, 10, -5, 5]}