1. WARM-UP Graph the equation below Graph the equation below y = ½ x + 3 y = ½ x + 3 Find 3 ordered pairs that are a solution to the equation above. Find 3 ordered pairs that are a solution to the equation above.

2. SECTION 6.5: GRAPHING LINEAR INEQUALITIES IN TWO VARIABLES

3. EXAMPLE 1 Check whether the ordered pair is a solution of 3x – 3y ≥ -2 Check whether the ordered pair is a solution of 3x – 3y ≥ -2 (0, 0) (0, 0) (0, 1) (0, 1)

4. GRAPHS OF LINEAR INEQUALITIES The graph of a linear inequality in two variables is the graph of the solutions of the inequality. The graph of a linear inequality in two variables is the graph of the solutions of the inequality.

5. GRAPH OF Y ≥ X+3 Every point in the shaded region and on the line is a solution of the inequality. Every point in the shaded region and on the line is a solution of the inequality. Every other point in the plane is not a solution. Every other point in the plane is not a solution.

6. GRAPHING LINEAR INEQUALITIES Step 1: Write inequality in slope-intercept form Step 1: Write inequality in slope-intercept form Step 2: Graph equation. Use a dashed line for. Use a solid line for ≥ or ≤. Step 2: Graph equation. Use a dashed line for. Use a solid line for ≥ or ≤. Step 3: Test a point in one of the half-planes to find whether it is a solution of the inequality. Step 3: Test a point in one of the half-planes to find whether it is a solution of the inequality. Step 4: If the test point is a solution, shade the half-plane it is in. If not, shade the other half- plane. Step 4: If the test point is a solution, shade the half-plane it is in. If not, shade the other half- plane.

7. EXAMPLE Graph y ≤ -2x + 1 Graph y ≤ -2x + 1

8. EXAMPLE Graph 9x – 3y ≥ 18 Graph 9x – 3y ≥ 18

9. EXAMPLE An interior decorator is going to remodel a kitchen. The wall above the stove and the counter is going to be redone as shown. The owners can spend $420 or less. Write a linear inequalities and graph the solutions. What are three possible prices for the wallpaper and tiles? An interior decorator is going to remodel a kitchen. The wall above the stove and the counter is going to be redone as shown. The owners can spend $420 or less. Write a linear inequalities and graph the solutions. What are three possible prices for the wallpaper and tiles?