Let’s organize our information!

3. Let’s organize our information!

4. Revenue Rent Month $400.00 $600.00 0 $410.00 $570.00 1 $420.00 $540.00 2

6. Let’s look at the data in a graph form!

7. Rent Revenue $600 $550 $500 $450 (5, 450) $400 0 8 2 4 6 10 12 Months

8. Rent Revenue These are called a linear functions. Why? $600 What do you call the place where two roads cross? Revenue $550 $500 Rent intersection $450 (5, 450) $400 0 8 2 4 6 10 12 Months

9. Rent Revenue Where does the revenue function begin? $600 Revenue $550 Where does the rent function begin? $500 Rent $450 (5, 450) $400 0 8 2 4 6 10 12 Months

10. Rent Revenue By looking at the graph, how can you tell which linear function is steeper? $600 Revenue $550 By looking at the table, how can you tell which linear function is steeper? $500 Rent $450 (5, 450) $400 0 8 2 4 6 10 12 Months

11. Rent Revenue By looking at the graph, how can you tell which linear function is decreasing? $600 Revenue $550 By looking at the table, how can you tell which linear function is decreasing? $500 Rent $450 (5, 450) $400 0 8 2 4 6 10 12 Months

12. Rent Revenue By looking at the graph, how can you tell which linear function is increasing? $600 Revenue $550 By looking at the table, how can you tell which linear function is increasing? $500 Rent $450 (5, 450) $400 0 8 2 4 6 10 12 Months

13. Rent Revenue How much does the rent function change each month? $600 Revenue $550 How does the graph show this change? $500 Rent How does the table show this change? $450 (5, 450) $400 0 8 2 4 6 10 12 Months

14. Rent Revenu How much does the revenue function change each month? $600 Revenue $550 How does the graph show this change? $500 Rent How does the table show this change? $450 (5, 450) $400 0 8 2 4 6 10 12 Months

15. Let’s look at the information in a symbolic/algebraic form!

18. What’s the pattern? Rent

19. Rent Revenue $600 $550 $500 Rent $450 (5, 450) $400 0 8 2 4 6 10 12 Months

20. Rent Revenue $600 $550 $500 Rent $450 (5, 450) $400 0 8 2 4 6 10 12 Months

21. What’s the pattern? Revenue

22. Rent Revenue $600 Revenue $550 $500 $450 (5, 450) $400 0 8 2 4 6 10 12 Months

23. Let’s get abstract!

24. y-axis Rent Revenue x-axis months

27. A B

28. C D

29. E F

30. Rent Revenue How can we find the intersection? $600 Revenue $550 $500 Rent intersection $450 (5, 450) $400 0 8 2 4 6 10 12 Months

33. Let’s solve algebraic systems of linear equations!

37. Let’s graph this baby!

40. Let’s graph this baby!

43. WHAT!!?? v

46. They are the SAME Line! Infinite Solutions

47. Solve it by solving for y in the first equation first.

48. Solve it by solving for x in the second equation first.

49. Is there another way to solve this?