There are three easy steps to graphing an inequality:

Isolate y: It'll be easiest to graph our inequality if $y$ is on it's own on one side of the equals sign. Something like this:$y>3x+5$ And remember, if you have something like $−y<3x+5$, when you divide both sides by $−1$, you need to flip the sign, so that you end up with $y>−3x−5$ Enter in an inequality to graph:

$y$

Graph it: Next step is to graph it! First, ignore the inequality, and pretend like you just have a normal equation.

Easiest way to draw the graph is to plug in different values for $x$, calculate the $y$-value, and plot the $(x,y)$ coordinates.

Shade it: Now that we have our line, we need to think about our inequality sign. The table below explains what each sign means.

Sign

Meaning

Dotted or Solid?

Above or Below?

<

Less Than

Dotted

Below

≤

Less Than or Equals

Solid

Below

>

Greater Than

Dotted

Above

≥

Greater Than or Equals

Solid

Above

If our sign includes "equals", that means $y$ can equal the values on our line, so we use a solid line.

If it doesn't include "equals", then we use a dotted line, since the values on our line aren't included.

And if $y$ is less than our line, then our possible values are all below the line, so we shade below.

If $y$ is greater than our line, then our possible values are all above the line, so we shade above.

Remember, our line is

So is our line dotted or solid?

Shaded above or below?

That's right! The final graph for the line you entered is here:

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