1. Lesson 6.7 Graph Linear Inequalities in Two Variables
Essential Question: How do you graph linear inequalities in two variables?

2. Before we start… Graph 𝑦=𝑥+1
Where do you think you would find solutions to 𝑦>𝑥+1?
Where do you think you would find solutions to 𝑦<𝑥+1?

3. What is a linear inequality in two variables?
It looks just like a linear equation but contains an inequality symbol instead.

4. What is a solution of a linear inequality in two variables?
An ordered pair (x, y) is a solution of a linear inequality in two variables if the inequality is true when the values of x and y are substituted into the inequality.

5. Which ordered pair is not a solution of 𝑥−3𝑦≤6?
b) 6,−1
c) 10,3 d) −1,2

6. Which ordered pair is a solution of 3𝑥+4𝑦>8?
a) 6,−3 b) 0,2
c) −2,−1 d) −3,5

7. Tell whether the ordered pair is a solution of −𝑥+2𝑦<8.
a) 0,0 b) 0,4
c) 3,5 d) −3,1

8. Tell whether the ordered pair is a solution of 5𝑥−2𝑦≤6.
a) 0,−4 b) 2,2
c) −3,8 d) −1,−7

9. What is the graph of a linear inequality in two variables?
The set of all points in a coordinate plane that represent solutions of the inequality.

11. How do you interpret graphs of linear inequalities in two variables?
A dashed boundary line means that points on the line are not solutions.
A solid boundary line means that points on the line are solutions.

12. How do you graph a linear inequality in two variables?
Graph the boundary line.
Use a dashed line for < or >
Use a solid line for ≤ or ≥
Shade the half plane that contains the solutions.
Shade above the line if it’s greater than
Shade below the line if it’s less than
Pick a test point to verify your solution.

24. What about linear inequalities in one variable?
The same rules apply for one variable inequalities as two variable inequalities.
Remember x results in a vertical line and y results in a horizontal line.

29. How do you graph linear inequalities in two variables?

30. Ticket Out the Door