How do you calculate the constant rate of change?

A 1400 gallon pool is being emptied at a rate of 350 gallons per hour.

In this lesson you will learn calculate the rate of change of a linear function by examining the four representations of a

function.

Let’s ReviewLet’s Review

Rate of change: Change in x-values

Change in y-values∆y

∆x

Let’s ReviewA Common Mistake

Students obtain the incorrect sign for slope

x y

-3 -1

-1 -7

0 -10

3 -19

-7 - -1-3 - -1

Slope =-7 - -1

-3 - -1

-6

-233 is incorrect

-7 - -1-1 - -3

-7 - -1

-1 - -3

-6

2-3 is correct

Let’s ReviewCore Lesson

A 1400 gallon pool is being emptied at a rate of 350 gallons per hour.

Constant rate of change = -350

Let W be the gallons remaining after T hours.

W = -350T + 1400

Constant rate of change = -350

Coefficient

Let’s ReviewCore Lesson

T (hours)

W (remaining

gallons)

0 1400

1 1050

2 700

3 350

1050 - 14001 – 0 -3501 -350

1-350

Constant rate of change =

Let’s ReviewCore Lesson

100100100

-700

2

-700

2Constant rate of change = -350

Let’s ReviewCore Lesson

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

Constant rate of change

y = 6x – 60

Constant rate of changeConstant rate of change =

x (hours)

y (total amount)

0 -60

1 -54

2 -48

3 -42

-54 - -601 – 0 61Constant rate of change = 6

30

5

30

56

In this lesson you have learned how to calculate the rate of

change of a linear function by examining the four

representations of a function.

Let’s ReviewGuided Practice

Jennifer made 100 necklaces and gave away 3 per week.

Identify the rate of change in each representation.y = -3 – 1.75x

x y

-4 -5

-1 2.5

2 10

4 15

Let’s ReviewExtension Activities

Save the grocery store circular ads or ask a friend for them. Find at least 5 items on sale (for example, 10 for $10) and calculate the rate of change for each one of that item.If possible, find the original rate of change. How much would you save buying 10 of that item on sale compared to the regular price?

http://www.grocerywiz.com/SundayAds.aspx

Let’s ReviewExtension Activities

The sophomore class is holding a fundraiser for their end of the year trip. How much money does a student earn for selling 1 keychain?

x (number of keychains sold)

y (money earned)

Prize Level

5 $6.25 School lanyard

20 $25.00 2 movie tickets

50 $62.50 $30 gift card

100 $125.00 mp3 player

Let’s ReviewQuick Quiz

Given the table of values, which choice shows the correct rate of change?

x y

-3 -6

-1 -8

3 -12

6 -15

a)

-1 - -3

-8 - 6

-3 - -1

-8 - -6d)

-1 - -3

-8 - -6c)

-1 - -3

-6 - -8b)

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 constant rate of change?