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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