1. Do Now 12/19/18 Copy HW in your planner. Text p. 271, #4-38 evens
In your notebook, explain how to graph the following lines; y = 4x – 3 and x + 2y = 0.
With your partner, complete Explorations #1, 2, & 3 on pages in your Student Journal.

2. Essential Question How can you graph a linear inequality in two variables?
With your partner, complete Explorations #1, 2, & 3 on pages in your Student Journal.

3. Learning Goal Learning Target
Students will be able to write and graph systems of linear equations.
Learning Target
Students will be able to graph linear equations and linear inequalities in two variables

4. Section 5.6 “Graph Linear Inequalities in Two Variables”
the result of replacing the = sign
in a linear equation with an inequality sign.
2x + 3y > 4
y ≥ 4x - 3
y ≤ ½x + 3
7y < 8x - 16

5. Linear Inequalities
An example of a linear inequality in two variables is x - 3y ≤ 6. The solution of an inequality in two variables, x and y, is an ordered pair (x, y) that produces a true statement when substituted into the inequality.
Which ordered pair is NOT a solution of x - 3y ≤ 6?
A. (0,0) B. (6,-1) C. (10, 3) D. (-1,2)
Substitute each point into the inequality. If the statement is true then it is a solution.
True, therefore
(0,0) is a solution.
x - 3y ≤ 6
(0) – 3(0) ≤ 6

6. Graph an Inequality in Two Variables
The graph of an inequality in two variables is the set of points that represent all solutions of the inequality.
The BOUNDARY LINE of a linear inequality divides the coordinate plane into two HALF-PLANES. Only one half-plane contains the points that represent the solutions to the inequality.

7. Graphing Linear Inequalities
Graphing Boundary Lines:
Use a dashed line for < or >.
Use a solid line for ≤ or ≥.

8. Graph the inequality y > 4x - 3.
Graph an Inequality
Graph the inequality y > 4x - 3.
STEP 2
STEP 3
STEP 1
Graph the equation
Test (0,0) in the original inequality.
Shade the half-plane that contains the point (0,0), because (0,0) is a solution to the inequality.

9. Graph the inequality x + 2y ≤ 0.
Graph an Inequality
Graph the inequality x + 2y ≤ 0.
STEP 2
STEP 3
STEP 1
Graph the equation
Test (1,0) in the original inequality.
Shade the half-plane that does not contain the point (1,0), because (1,0) is not a solution to the inequality.

10. Graph the inequality x + 3y ≥ -1.
Graph an Inequality
Graph the inequality x + 3y ≥ -1.
STEP 2
STEP 3
STEP 1
Shade the half-plane that contains the point (1,0), because (1,0) is a solution to the inequality.
Graph the equation
Test (1,0) in the original inequality.

11. Graph the inequality y ≥ -3.
Graph an Inequality
Graph the inequality y ≥ -3.
STEP 2
STEP 3
STEP 1
Shade the half-plane that contains the point (2,0), because (2,0) is a solution to the inequality.
Graph the equation
Test (2,0) in the original inequality. Use only the y-coordinate, because the inequality does not have a x-variable.

12. Graph the inequality x ≤ -1.
Graph an Inequality
Graph the inequality x ≤ -1.
STEP 2
STEP 3
STEP 1
Shade the half-plane that does not contain the point (3,0), because (3,0) is not a solution to the inequality.
Graph the equation
Test (3,0) in the original inequality. Use only the y-coordinate, because the inequality does not have a x-variable.

13. Challenge “Can You Write and Graph the Mystery Inequality???”
The points (2,5) and (-3, -5) lie on the boundary line. The points (6,5) and (-2, -3) are solutions of the inequality.
y ≤ 2x + 1

14. You can spend at most $10 on grapes and apples for a fruit salad
You can spend at most $10 on grapes and apples for a fruit salad. Grapes cost $2.50 per pound, and apples cost $1 per pound. Write an graph an inequality that represents the amounts of grapes and apples you can buy.

15. Graphing Calculator
Homework
Text p. 271, #4-38 evens

16. Educreations.com