Linear inequality in two variables The result of replacing the = sign in a linear equation with <, ≤, >, or ≥ .

Solution of an inequality in two variables An ordered pair (x, y) that produces a true statement when the values of x and y are substituted into the inequality.

Graph of an inequality in two variables The set of points that represent all solutions of the inequality

Half-plane Either half of the coordinated plane that is divided by the boundary line of a linear inequality.

Example 1: Check solutions of a linear inequality

Tell whether the ordered pair is a solution of 2x – 3y > 5. a. ( 4, 1 ) b. ( 2, -2)

SOLUTION a. ( 4, 1 ) Step 1 Write the inequality.

Step 2 Substitute the values of the ordered pair.

Step 3 Simplify

Example 2: Graph a linear inequality in two variables

Graph the inequality Graph the inequality yy>4>4xx-2-2SOLUTION Step 1 Graph the equation. Step 2 Test a point not on the boundary line.

Step 3 Shade the half-plane containing the point if the ordered pair is a solution of the inequality. Shade the other half-plane if the ordered pair is not a solution.

Example 3: Graph a linear inequality in one variableGraph the inequality y≥-4.

SOLUTIONStep 1 Graph the equation Step 2 Test a point

Step 3 Shade

TRY ON YOUR OWNTRY ON YOUR OWNGraph the inequality.Graph the inequality.2. 2. yy<3<3xx-4 -4

3. x< -2

Example 4: Multiple Choice Practice

HOMEWORK: Textbook p. 429- # 3-6 all, 19-22 all