1. In this lesson… We will write and graph linear inequalities

2. Sharon earns $8 an hour and a bonus of $24 each week. Write an equation describing Sharon’s weekly pay.

3. Complete the table: HoursProcessTotal Pay 0 1 2 3 xy

4. Complete the table: HoursProcessTotal Pay 08(0) + 2424 18(1) + 2432 28(2) + 2440 38(3) + 2448 x8x + 24y

5. An equation to describe the total weekly earnings in terms of the number of hours worked is… y = 8x + 24 The amount Sharon needs to pay all of her bills must be less than or equal to the amount she earns

6. An inequality to describe the amount Sharon needs to earn to pay her bills is … Graph this Inequality

7. Begin at the y-intercept hours Bills ($) 8 1 2 3 4 5 16 24 32 40

8. Find a 2 nd point with the slope hours Bills ($) 8 1 2 3 4 5 16 24 32 40

9. Connect the points with a line hours Bills ($) 8 1 2 3 4 5 16 24 32 40

10. Shade below the line hours Bills ($) 8 1 2 3 4 5 16 24 32 40 The shaded region represents the the amounts Sharon can afford

11. Paul claims he can run 4 miles a day. He has already run 32 miles this month. An equation describing the total number of miles that Paul has run in terms of the days is y = 4x + 32

12. Paul’s coach insists he run more than 4 miles each day to prepare to run in a marathon. Write an inequality describing the total miles the coach wants Paul to run.

13. The inequality shows the total miles, y, is greater than 4x + 32 y > 4x + 32 Graph this inequality

14. First Graph the y-intercept days Total Miles 4 1 2 3 4 5 8 12 16 24 32 36 40

15. Graph a second point days Total Miles 4 1 2 3 4 5 8 12 16 24 32 36 40

16. Connect with a dotted line days Total Miles 4 1 2 3 4 5 8 12 16 24 32 36 40 The points on the line are not included since Paul must jog MORE than the amounts on the line

17. Shade ABOVE the line days Total Miles 4 1 2 3 4 5 8 12 16 24 32 36 40 The shaded region represents the miles Paul must run

18. The Student Council is purchasing T-shirts and Posters to sell for a school fundraiser Each T-Shirt costs $6 and each poster costs $2

19. The Student Council Sponsor says that they must keep their spending below $120 for this fundraiser If T is the number of T- shirts, then 6T is the cost for all the T-Shirts

20. If P is the number of posters, then 2P is the cost for all the posters Since they must spend less than $120, the inequality for this problem is… 6T + 2P < 120

21. To graph this inequality, we can use T and P intercepts 6T + 2P < 120 TP 0 0

22. To graph this inequality, we can use T and P intercepts 6T + 2P < 120 TP 200 060

23. Graph each ordered pair Posters 10 5 10 15 20 25 20 30 40 50 TP 200 060 T-Shirts 60 6T + 2P < 120

24. Connect with a dotted line Posters 10 5 10 15 20 25 20 30 40 50 TP 200 060 T-Shirts 60 6T + 2P < 120

25. Shade below the line Posters 10 5 10 15 20 25 20 30 40 50 TP 200 060 T-Shirts 60 6T + 2P < 120

26. The shaded region represents the numbers of T-Shirts and Posters the Student Council can afford Posters 10 5 10 15 20 25 20 30 40 50 T-Shirts 60 Can they afford 15 T-Shirts and 30 posters?

27. Complete Activity 6d Write Linear Inequalities Graph Linear Inequalities Solve Problems using Linear Inequalities