warm-up graph the equation below graph the equation below y = ½ x + 3 y = ½ x + 3 find 3 ordered...

WARM-UPWARM-UP

• Graph the equation belowGraph the equation below•y = ½ x + 3y = ½ x + 3

• Find 3 ordered pairs that are a solution to the Find 3 ordered pairs that are a solution to the equation aboveequation above. .

SECTION 6.5: GRAPHING SECTION 6.5: GRAPHING LINEAR INEQUALITIES IN LINEAR INEQUALITIES IN

TWO VARIABLESTWO VARIABLES

EXAMPLE 1EXAMPLE 1

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

GRAPHS OF LINEAR GRAPHS OF LINEAR INEQUALITIESINEQUALITIES

• The graph of a linear inequality in two The graph of a linear inequality in two variables is the graph of the solutions of variables is the graph of the solutions of the inequality.the inequality.

GRAPH OF Y ≥ X+3GRAPH OF Y ≥ X+3• Every point in the Every point in the

shaded region shaded region and on the line is and on the line is a solution of the a solution of the inequality.inequality.• Every other point Every other point

in the plane is in the plane is not a solution. not a solution.

GRAPHING LINEAR GRAPHING LINEAR INEQUALITIESINEQUALITIES

• Step 1: Write inequality in slope-Step 1: Write inequality in slope-intercept formintercept form• Step 2: Graph equation. Use a dashed Step 2: Graph equation. Use a dashed

line for < or >. Use a solid line for ≥ or line for < or >. Use a solid line for ≥ or ≤.≤.• Step 3: Test a point in one of the half-Step 3: Test a point in one of the half-

planes to find whether it is a solution of planes to find whether it is a solution of the inequality.the inequality.• Step 4: If the test point is a solution, Step 4: If the test point is a solution,

shade the half-plane it is in. If not, shade shade the half-plane it is in. If not, shade the other half-plane. the other half-plane.

EXAMPLEEXAMPLE• Graph y ≤ -2x + 1Graph y ≤ -2x + 1

EXAMPLEEXAMPLE• Graph 9x – 3y ≥ 18Graph 9x – 3y ≥ 18

EXAMPLEEXAMPLE• An interior decorator is going to remodel a An interior decorator is going to remodel a

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