1. How do you know the initial value of a linear relation? A 1400 gallon pool is emptied at a rate of 350 gallons per hour.

2. In this lesson you will learn how to determine the initial value of a linear function by interpreting all four representations of a function.

3. Let’s Review An ice cream cup is $2.00 plus $0.50 for each additional topping. x (toppings) y (cost) 0$2.00 1$2.50 2$3.00 3$3.50 Initial value = $2.00

4. Let’s Review A Common Mistake An ice cream cup is $2.00 plus $0.50 for each additional topping. Initial value = 0.50Incorrect! Initial value = 2.00 It happens 1 time, with 0 toppings!

5. Let’s Review Core Lesson A 1400 gallon pool is being emptied at a rate of 350 gallons per hour. Initial value = 1400 Let W be the gallons remaining after T hours. W = -350T + 1400 Initial value = 1400 Constant

6. Let’s Review Core Lesson T (hours) W (remaining gallons) 01400 11050 2700 3350 1400Initial value =

7. Let’s Review Core Lesson 100 Initial value =1400

8. Let’s Review Core Lesson William purchased a $60 bicycle and he will earn $6 per hour delivering newspapers. Initial value = -60 y = 6x – 60 Initial value = -60 Initial value = x (hours) y (total amount) 0-60 1-54 2-48 3-42 Initial value =-60

9. In this lesson you have learned how to determine the initial value of a linear function by interpreting all four representations of a function

10. Let’s Review Guided Practice Jennifer made 100 necklaces and gave away 3 per week. Identify the initial value in each representation. y = -3 – 1.75x xy -4-5 2.5 210 415

11. Let’s Review Extension Activities A glider takes 90 minutes to land. The position (P), in feet, at any given time (t) can be found using the equation: P = -5(t – 90) What was the initial height (value) of the glider at takeoff?

12. Let’s Review Extension Activities Running back Joseph Addai signed a contract with the New England Patriots worth $725,000 per year plus a $75,000 signing bonus. What is the initial value of that contract? Explain.

13. Let’s Review Quick Quiz Given the table of values, which choice shows the correct initial value? xy -3-6 -8 3-12 6-15 a) -6 d) -10 c) -9 b) -8

14. Let’s Review Quick Quiz The high school senior class planned a graduation reception for parents and friends at a local restaurant. They held fund-raisers during their 12th grade year to raise the money. The restaurant charges $150 for the room and $10 per person for food and drinks. What is the initial value?