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

Mar 19, 2017

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

$3 x - y < 2$

Add $y$ to both sides:

$3 x < 2 + y$

Subtract $2$ from both sides:

$3 x - 2 < y$

Flip the order of the equation:

$y > 3 x - 2$

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

The line $y = 3 x - 2$:

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

The inequality $y > 3 x - 2$:

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