how can you use a graph to determine whether two rates are the same? for example: on saturday, jen...

How can you use a graph to determine whether two rates are the same?

For example:On Saturday, Jen walked 2.4 miles in 45

minutes. On Sunday, Jen walked 3.2 miles in 60 minutes. Did Jen walk at

the same rate on Saturday and Sunday?

In this lesson you will learn how to determine if two rates are equivalent by graphing.

Let’s Review

oranges total fruit

= oranges:total fruit

applesoranges

= apples:oranges

Ratios

Let’s Review

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

-6

-4

-2

0

2

4

6

(2,5)

(2,-5)

(-2,5)

(-2,-5)

y

x

A Common Mistake

(x,y)

Up or down?Left or right?

Positive xNegative x

Positive y

Negative y

Core Lesson

Graphing Jen’s Walking Rate:

Let x = time spent walking

Let y = distance walked

Core Lesson

Time(mins.)

Distance(miles)

45

60

2.4

3.2 Dis

tance

(m

iles)

Time (mins.)

Jen’s Walking Rate

6543210

0 15 30 45 60

(45,2.4)

(60,3.2)

Core Lesson

Time(hours)

Distance(miles)

0.75

1

2.4

3.2 Dis

tance

(m

iles)

Time (hours)

Jen’s Walking Rate

6543210

0 .25 .50 .75 1

(0.75,2.4)

(1,3.2)

Core Lesson

Graphs of Equivalent Rates:

Begin at the Origin

Form a Straight Line

In this lesson you have learned how to determine if two rates are equivalent by graphing.

Guided Practice Let x = parts of yellow Let y = parts of blue Graph the data in the table to determine which green paint mixtures have equivalent ratios of x:y

Paint Parts of Yellow Parts of Blue

A 1 2

B 2 3

C 3 6

D 4 6

E 5 8

F 6 9

Guided Practice

0 1 2 3 4 5 6 70123456789

10

Green Paint Mixtures

Blue

Yellow

A (1,2)B (2,3)

C (3,6)

D (4,6)

F (6,9)E (5,8)

Guided Practice Compare Ratios of Parts Yellow : Parts Blue

A & C =

1:2

0

1

B, D & F = 2:3

0

1

E = 5:8

0

1

Extension Activities

Create three shades of green paint by mixing different parts of yellow and green paint. Record the parts of yellow and green that you used in a table. Graph the data from your table. Write three equations for your green paint mixtures.

Extension Activities

Paint Parts of Red Parts of Yellow

A 2 0

B 4 2

C 3 3

D 3 6

E 0 1

Create the following paint mixtures. List the paints from the most red to the most yellow.

Quick Quiz Let x = parts of red y = parts of blue

Graph the data in the table to determine which purple paint mixtures have the same ratio?

Paint Parts of Red Parts of Blue

A 1 6

B 2 8

C 3 18

D 4 24

E 5 20

F 6 18