2-7 Graphing Inequalities

ObjectivesStudents will be able to:

1) graph linear inequalities2) graph absolute value inequalities

Linear inequalities

• A linear inequality resembles a linear equation, but with an inequality symbol, rather than an equal sign.

• The graph of a linear inequality is the region of the graph in which every point in the region satisfies the inequality. This region gets shaded.

A linear inequality can be graphed by following these steps:

1) Determine whether the boundary (the line) should be solid or dashed. Then graph the boundary.

or means solid boundary< or > means dashed boundary2) Choose a point not on the boundary and

test it in the inequality. [(0, 0) is my suggestion] 3) If a true inequality results, shade the region containing your test point.

If a false inequality results, shade the other region.

Example 1: Graph each inequality.

Step 1: Graph y=2x+1; However, since the symbol is >, the line should be dashed.Step 2: Test (0, 0)

Step 3: Shade your region!

Try this.

Maintain your composure, and give this a shot.

Try this on for size.

Absolute value inequalities

• Now that you are having the most fun you have ever had in your entire life, EVER, let’s look at absolute value inequalities.

• Graphing absolute value inequalities is done following the same procedure as graphing linear inequalities. Start by graphing the absolute value function (same rules for solid or dashed). Then pick a test point, and finally shade the region that works.

Example 2: Graph each absolute value inequality.

Try this.

One more.