# How do you graph inequalities on a coordinate plane?

Apr 1, 2015

You should remember how to graph $y = x$ and $y = - x$. So if you don't know, have a look at them from the internet.

$G i v e n :$ ax+b ? 0
Where ? represents the inequality sign.

How to graph inequalities:

• Determine $a$ is either positive or negative.

• If $a$ is positive then your base graph will look like $y = a x$, else it will look like $y = - \left\mid a \right\mid x$

• $b$ tells you that how much you need to move your base graph on the coordinate plane. If $b$ is positive, move your graph in $+ y$ direction, else $- y$ direction. When $x = 0$, $y$ should be equal to $b$.

• If ? sign is $\ge$ or $\le$ your graph should be straight not dashed. Because $y$ can be equal to those values.

• If ? sign is $>$ or $<$ your graph should be dashed. Because $y$ cannot be equal to anything.

• Take any point from the coordinate plane that is not on your graph. Test it in the given inequality. If that point satisfies the inequality then shade your graph in that points's direction. Else, shade otherwise.