Question

How do you graph the inequality `3x - y < 2`?

Answer 1

We can make this look like the linear equation `y=mx+b`, except it will either look like `y>mx+b` or `y < mx+b`.

The inequality we start with is:

`3x-y < 2`

Add `y` to both sides:

`3x < 2+y`

Subtract `2` from both sides:

`3x-2 < y`

Flip the order of the equation:

`y > 3x-2`

So, we graph the line `y=3x-2`. Since we want to find when `y` is greater than this, shade above the line. We leave the line `y=3x-2` dashed to show it is not included in the inequality. If we had the inequality `y>=3x-2`.

The line `y=3x-2`:

graph{3x-2 [-5, 5, -20, 20]}

The inequality `y > 3x-2`:

graph{y>3x-2 [-5, 5, -20, 20]}