Graphing an inequality involves two main steps.

Plotting the boundary line.
Shading half of the plane to show the solution set.

Boundary Line

To graph the inequality, we have to draw the boundary line. The equation of a boundary line is written by replacing the inequality symbol from the inequality with an equals sign.

Inequality	Boundary Line
$y < - 4$	$y = - 4$

Notice that the equation for this boundary line only has one variable. This equation is telling us that each and every point that lies on the line will have a $y -$ coordinate equal to $- 4 .$ This means that it is a horizontal line. Also, the inequality is strict, so the points on the boundary line are not included in the solution set. We show this by drawing a dashed line.

Shading the Plane

The inequality $y < - 4$ describes all values of $y$ that are less than $- 4 .$ This means that every possible $(x, y)$ coordinate pair with a $y -$ value that is less than $- 4$ needs to be included in the shading. In other words, we will shade the region below the boundary line.

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