1. Chapter 4.6
Construct Functions

2. How can we model relationships between quantities?
??? Essential Question ???
How can we model relationships between quantities?

3. Turn to page 319 in your workbook
Real-World Link
Turn to page 319 in your workbook

4. Initial Value
REMEMBER
The initial value of a function is the corresponding y-value when x equals 0.

5. Example 1
The shoe store offers free points when you sign up for their rewards card. Then, for each pair of shoes purchased, you earn an additional number of points. The graph shows the total points earned for several pairs of shoes. Find and interpret the rate of change and initial value.

6. Example 1 Continued Rate of change: Interpretation:
Initial value:
90−60 4−2
= 30 2
=15
You get 15 points per pair of shoes purchased. 30
You get 30 free points for signing up.

7. Music Inc. charges a yearly subscription fee plus a monthly fee
Music Inc. charges a yearly subscription fee plus a monthly fee. The total cost for different numbers of months, including the yearly fee, is shown in the graph. Find and interpret the rate of change and initial value.

8. Rate of change: Interpretation: Initial value: The monthly fee is $3.
18−15 2−1
= 3 1 =3
The monthly fee is $3.
𝑦=𝑚𝑥+𝑏
15=3(1)+𝑏
𝑏=12
The yearly fee is $12.

9. Example 2
Joan has some photos in her photo album. Each week she plans to add 12 photos. Joan had 120 photos after 8 weeks. Assume the relationship is linear. Find and interpret the rate of change and initial value.
Rate of change:
“12 photos per week” 𝑝ℎ𝑜𝑡𝑜𝑠 1 𝑤𝑒𝑒𝑘 =12
Initial value:
𝑦=𝑚𝑥+𝑏
120=12 8 +𝑏
𝑏=24
Interpretation:
The initial number of photos in the album is 24.

10. A zoo charges a rental fee plus $2 per hour for strollers
A zoo charges a rental fee plus $2 per hour for strollers. The total cost of 5 hours is $13. Assume the relationship is linear. Find and interpret the rate of change and initial value.
Rate of change:
“Cost per hour” $2 1 ℎ𝑜𝑢𝑟 =2
Initial value:
𝑦=𝑚𝑥+𝑏
13=2 5 +𝑏
𝑏=3
Interpretation:
The rental fee is $3.

11. Example 3
The table shows how much money Ava has saved. Assume the relationship between the two quantities is linear. Find and interpret the rate of change and initial value.

12. Example 3 Continued Initial Value: 𝑦=𝑚𝑥+𝑏 110=20 3 +𝑏 𝑏=50 +20 +1
Interpretation: +1
+20 +1
+20 +1
+20
Ava had initially saved $50.
20 1 =20
Rate of change:
Interpretation:
Ava saves $20 a month

13. The table shows the monthly cost of sending text messages
The table shows the monthly cost of sending text messages. Assume the relationship between the two quantities is linear. Find the rate of change ad initial value.
Initial Value:
Interpretation:
$10
Rate of change:
Interpretation:
$0.10
Each text costs $0.10.
The initial phone plan costs $10.

14. Exit Ticket

15. Chapter 4.6
Construct Functions

16. How can we model relationships between quantities?
??? Essential Question ???
How can we model relationships between quantities?

17. Turn to page 319 in your workbook
Real-World Link
Turn to page 319 in your workbook

18. Initial Value
REMEMBER
The initial value of a function is the corresponding y-value when x equals 0.

19. Example 1
The shoe store offers free points when you sign up for their rewards card. Then, for each pair of shoes purchased, you earn an additional number of points. The graph shows the total points earned for several pairs of shoes. Find and interpret the rate of change and initial value.

20. Example 1 Continued
Rate of change:
Interpretation:
Initial value:

21. Music Inc. charges a yearly subscription fee plus a monthly fee
Music Inc. charges a yearly subscription fee plus a monthly fee. The total cost for different numbers of months, including the yearly fee, is shown in the graph. Find and interpret the rate of change and initial value.

22. Rate of change:
Interpretation:
Initial value:

23. Example 2
Joan has some photos in her photo album. Each week she plans to add 12 photos. Joan had 120 photos after 8 weeks. Assume the relationship is linear. Find and interpret the rate of change and initial value.
Rate of change:
Initial value:
Interpretation:

24. A zoo charges a rental fee plus $2 per hour for strollers
A zoo charges a rental fee plus $2 per hour for strollers. The total cost of 5 hours is $13. Assume the relationship is linear. Find and interpret the rate of change and initial value.
Rate of change:
Initial value:
Interpretation:

25. Example 3
The table shows how much money Ava has saved. Assume the relationship between the two quantities is linear. Find and interpret the rate of change and initial value.

26. Example 3 Continued Initial Value: Interpretation: Rate of change:

27. The table shows the monthly cost of sending text messages
The table shows the monthly cost of sending text messages. Assume the relationship between the two quantities is linear. Find the rate of change ad initial value.
Initial Value:
Interpretation:
Rate of change:
Interpretation:

28. Exit Ticket