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.

\underline{Inequality} y \leq 5 \underline{Boundary Line} y = 5

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

5 .

This means that it is a horizontal line. Notice that the inequality is not strict, so the points on the boundary line are included in the solution set. We have shown this by drawing a solid line.

Shading the Plane

The inequality $y \leq 5$ describes all values of $y$ that are less than or equal to $5 .$ This means that every possible $(x, y)$ coordinate pair with a $y -$ value that is less than or equal to $5$ needs to be included in the shading.

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