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.

In this lesson you will learn how to determine the initial value of a linear function by

interpreting all four representations of a function.

Let’s ReviewLet’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

Let’s ReviewA 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!

Let’s ReviewCore 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

Let’s ReviewCore Lesson

T (hours)

W (remaining

gallons)

0 1400

1 1050

2 700

3 350

1400Initial value =

Let’s ReviewCore Lesson

100100

Initial value = 1400

Let’s ReviewCore Lesson

William purchased a $60 bicycle and he will earn $6 per hour delivering newspapers.

Initial value = -60

y = 6x – 60

Initial value = -60Initial value =

x (hours)

y (total amount)

0 -60

1 -54

2 -48

3 -42

Initial value = -60-60

In this lesson you have learned how to determine the initial value of a linear function by

interpreting all four representations of a function

Let’s ReviewGuided Practice

Jennifer made 100 necklaces and gave away 3 per week.

Identify the initial value in each representation.y = -3 – 1.75x

x y

-4 -5

-1 2.5

2 10

4 15

Let’s ReviewExtension 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?

Let’s ReviewExtension 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.

Let’s ReviewQuick Quiz

Given the table of values, which choice shows the correct initial value?

x y

-3 -6

-1 -8

3 -12

6 -15

a) -6

d) -10

c) -9

b) -8

Let’s ReviewQuick 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?