Graphing Two-Variable Inequalities (Day 7)

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

plane.

Wednesday, April 19, 2023

The graph of: y =-2x+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?

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.

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.

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

x substitute to the output

y

-1

0

1

2

3

3(-1) – 5

-3-53(0) – 5

0-53(1) – 5

3-53(2) – 5

6-53(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!

Graphing Two-Variable Inequalities

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