Graphing Inequalities: The Basics

An equation like $y = 2x + 1$ draws a line. An inequality like $y > 2x + 1$ draws a whole region, which is a shaded area on one side of that line.

Every graph like this has exactly two decisions. The first is the line type. The line itself is called the boundary line. If the sign has a small line underneath it, meaning greater than or equal to, or less than or equal to, then points on the line count and you draw a solid line. If the sign has no line underneath, points on the line do not count and you draw a dashed line.

The second decision is the shading. Get $y$ alone on the left. Greater than means shade above the line. Less than means shade below it.

When you are unsure, test the point $(0, 0)$ and see if it makes the inequality true.