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### Graphing Two-Variable Inequalities (Day 7)

We are learning to…graph inequalities with two variables on a coordinate plane.

Wednesday, March 12, 2014

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?

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?

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?

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.

Name two different way that the graph of y < -2x + 3 is different from the graph of y ≥ -2x + 3.

How can we show that solutions are not on the line?

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.

Graph the inequality y < 3x - 5

Test:

Above the line

(0, 0)

3(-1) – 5

-3-5

-1

-8

0 < 3(0) - 5

3(0) – 5

0-5

0

-5

0 < -5

3(1) – 5

3-5

Below the line

(7, 0)

1

-2

3(2) – 5

6-5

2

0 < 3(7) - 5

1

0 < 16

3(3) – 5

9-5

Will the line be solid or broken?

3

4

Shade below the line!

BROKEN LINE!

Graphing Two-Variable Inequalities

- Try graphing a few inequalities with two variables with your team.

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