Question

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

Answer 1

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

`3x + 2y > 5`

`2y > -2x + 5 |:2`

`y > -3/2x + 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 = -3/2x + 5/2`

So,

`x = 0 => y = +5/2`

`y = 0 => 0 = -3/2x + 5 => x = 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`-3/2x + 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]}