1. Chapter 6 – Solving and Graphing Linear inequalities
6.5 – Graphing Linear Inequalities in Two Variables

2. 6.5 – Graphing Linear Inequalities in Two Variables
Today we will be learning how to:
Graph a linear inequality in two variables
Model a real-life situation using a linear inequality in two variables

3. 6.5 – Graphing Linear Inequalities in Two Variables
A linear inequality in x and y is an inequality that can be written with >, ≥, <, or ≤.

4. 6.5 – Graphing Linear Inequalities in Two Variables
An ordered pair (x, y) is a solution of a linear inequality when the values of x and y are substituted into the inequality and the result is true.

5. 6.5 – Graphing Linear Inequalities in Two Variables
Example 1
Check whether the ordered pair is a solution of 4x + 5y ≤ 12.
(-3, 5)
(0, 2)
(6, -8)

6. 6.5 – Graphing Linear Inequalities in Two Variables
The graph of a linear inequality in two variables is the graph of the solutions of the inequality.
The graph of 2x – 3y ≥ -2 is shown.
Every point in the shaded region and on the line is a solution of the inequality.
Every other point is not a solution.

7. 6.5 – Graphing Linear Inequalities in Two Variables
GRAPHING A LINEAR INEQUALITY
Graph the corresponding equation (y = mx + b)
Use a dashed line for inequalities with > or <
Use a solid line for inequalities with ≥ or ≤.
The line you drew separates the coordinate plane into two half-planes.
If the symbol is > or ≥, shade above the line.
If the symbol is < or ≤, shade below the line.

8. 6.5 – Graphing Linear Inequalities in Two Variables
Example 2
Sketch the graph of x ≥ 1.

9. 6.5 – Graphing Linear Inequalities in Two Variables
Example 3
Sketch the graph of y > -3.

10. 6.5 – Graphing Linear Inequalities in Two Variables
Example 4
Sketch the graph of x – y ≤ 2.

11. 6.5 – Graphing Linear Inequalities in Two Variables
Example 5
Sketch the graph of y + x > -1.

12. 6.5 – Graphing Linear Inequalities in Two Variables
HOMEWORK
Page 363
#24 – 52 even

13. 6.5 – Graphing Linear Inequalities in Two Variables
HOMEWORK
Page 364
#43 – 48, 50 – 60 even