1. Graphing Two-Variable Inequalities (Day 7) We are learning to…graph inequalities with two variables on a coordinate plane. Thursday, August 06, 2015

2. The graph of: y =-2x+3

3. Graphing Two-Variable Inequalities Is (-1, 5) a solution to the function? How can you tell by just using the graph? How can you tell by the equation? Is (2, -1) a solution to the function? What about (0, 0)? What determines if a points lies on the line? What is the different between the points on the line and the points not on the line?

4. The graph of: y ≥-2x+3 Your team will be given a list of points to test in the inequality y ≥ -2x+3. For each point that makes the inequality true put a point on the board using a marker for our class graph. How could we accurately show ALL the solutions are to this inequality on the graph?

5. Graphing Two-Variable Inequalities With your teammates predict what the inequality y < -2x + 3 will look like when it is graphed on a coordinate plane? How will the graph of y < -2x + 3 be different from the graph of y ≥ -2x + 3?

6. The graph of: y <-2x+3 Test your points again for the inequality y < -2x+3. For each point that makes the inequality true put a point on the board using a marker for our class graph. How can we show that solutions are not on the line? Name two different way that the graph of y < -2x + 3 is different from the graph of y ≥ -2x + 3.

7. Graphing Two-Variable Inequalities Steps for graphing inequalities with two variables: Step 1: Find inputs and outputs for the inequality and plot them on the coordinate plane Step 2: Decide if the line needs to be solid or broken (dashed) If > or < then use a broken line If ≥ or ≤ then use a solid line Step 3: Choose a point above the line and below the line and test each in the inequality. Step 4: Shade the correct solution area on the graph.

8. Graph the inequality y < 3x - 5 xsubstitute to the output y 0 1 2 3 3(-1) – 5 -3-5 3(0) – 5 0-5 3(1) – 5 3-5 3(2) – 5 6-5 3(3) – 5 9-5 -8 -5 -2 1 4 Will the line be solid or broken? Test: BROKEN LINE! Above the line (0, 0) 0 < 3(0) - 5 0 < -5 Below the line (7, 0) 0 < 3(7) - 5 0 < 16 Shade below the line!

9. Graphing Two-Variable Inequalities Try graphing a few inequalities with two variables with your team.