1. Chapter 7.5

2. Graphing Systems of Inequalities Lesson Objective: NCSCOS 2.01 Students will know how to graph a system of linear inequalities

3. Graphing Systems of Inequalities Graph the line 4x – 2y > 6 We can start this problem as if it were an equals sign First we have to put the equation in slope-intercept form (y= mx + b) in order to graph it

4. Graphing Systems of Inequalities Subtract 4x from both sides I always write the x first so it looks like my formula Divide both sides by -2 Don’t forget, the sign flips when you divide by a negative!

5. Graphing Systems of Inequalities In order to graph, we begin with the b -3 means this line passes through the y-axis at -3 Put a point at (0, -3)

6. Graphing Systems of Inequalities We then need to use the slope to find the next point The slope as a fraction is Y’s are on top, and they make the point go up and down 2121

7. Graphing Systems of Inequalities Since the 2 is positive we move up 2 The bottom number is the x value This makes the point move left and right Since the 1 is positive we move one to the right

8. Graphing Systems of Inequalities Connect the dots! For this problem, since y is not equal to 2x-3, the solution cannot be on the line To represent this, we use a dotted line instead of a solid one

9. Graphing Systems of Inequalities This problem also says that y values are smaller than 2x – 3 Let’s see what that means

10. Graphing Systems of Inequalities If we plug in a value for x let’s see what we get! Let’s plug in 1 for x Solve Y is less than -1 when x is 1 Look at it on the graph

11. Graphing Systems of Inequalities What values of y are less than -1 when x is 1? Any number below the point (1, -1) The same this happens for all values of x that you pick, y will be below the line

12. Graphing Systems of Inequalities Therefore, y will always be below the dotted line To show this, we shade the graph below the dotted line The answer can be any point where it’s shaded

13. Graphing Systems of Inequalities Example: Find the solution of the following two inequalities: Since these are inequalities, we need to find the area where they both are shaded

14. Graphing Systems of Inequalities Begin with the b Use the slope to find the second point Connect the dots with a dotted line Shade the area below the line

15. Graphing Systems of Inequalities Begin with the b Use the slope to find the second point Connect the dots This time we use a solid line because the answer can be on the line Since y is less than we have to shade below this line also

16. Graphing Systems of Inequalities The solutions to this problem is in the green area where both equations are shaded. Let’s pick a point and see what happens (2, -2) should make each equation work

17. Graphing Systems of Inequalities Plug in the point and see! Since the point solves both equations it works as an answer!

18. Graphing Systems of Inequalities Look at the point again

19. Graphing Systems of Inequalities 1. What’s the equation of line a? 2. What’s the equation of line b? 3. Is (2, 1) a solution? 4. Is (-2, 1) a solution? 5. Is (-1, 1) a solution? a b

20. Graphing Systems of Inequalities 1. What’s the equation of line a? 2. What’s the equation of line b? 3. Is (2, 1) a solution? 4. Is (-2, 1) a solution? 5. Is (-1, 1) a solution? a b y > x + 2 y ≤ -x No Yes

21. Graphing Systems of Inequalities 1. y ≤ 3x + 2 and y < -3x + 8 2. y > -1/2x – 1 and y ≤ 1/3x + 4 3. y < -4x + 7 and y ≥ 2x – 5 4. 4x – 2y ≤ -2 and 6x - 3y > -9