How can you show an infinite number of possible answers?

Egg salad: 2 pound for $6How much is one pound of egg salad? How about 6 pounds? You can display all the possibilities in a

proportional relationship by graphing!

1 pound for $5

2 pounds for $6

20 pounds for $100

1 pound for $3

6 pounds for $18

Let’s Review

Core Lesson

2 pounds for $6Weight

(lb.)Cost ($)

2

4

6

6

12

18

Let’s Review

Core Lesson

Weight (lb.)(x)

Cost ($)(y)

2

4

6

6

12

18

Weight (lb.)

Proportional vs. Non-Proportional• If two quantities are proportional, then

they have a constant ratio. – To have a constant ratio means two quantities

have the same unit rate.

• If the ratio is not constant, the two quantities are said to be non-proportional.– So, the two quantities do not have the same

unit rate.

Proportional Relationships• Will always go through the origin on a graph.

(0,0)• Graph will always be a straight line.

In order to tell if a graph is proportional the line must go through the origin.

Tell if the following graphs represent a proportional relationships.

1 2 3 4 5

1

2

3

4

5

x

y

1 2 3 4 5

1

2

3

4

5

x

y

Proportional ? _________ Proportional ? _________

Why?Line goes through the origin

Why? Line does notgo through the origin

Yes No

Let’s Review

Core Lesson

Weight (lb.)(x)

Cost ($)(y)

2

4

6

6

12

18

Weight (lb.)Is the weight of the egg salad proportional to the cost? Yes

Let’s ReviewGuided Practice

Graph the proportional relationship “2 pounds of prime rib for $11.”

Weight (lb.)

Weight (lb.)(x)

Cost ($)(y)

112

1 5.504 22

Is the weight of the prime rib proportional to the cost? Yes

Let’s ReviewGuided Practice

State in words the proportional relationship shown here.(There are many correct answers!)

x

y

Time (min.)

2 feet per min

Let’s Review

Quick Quiz

State in words the proportional relationship shown here.(There are many correct answers!)

Weight (ounces)

You Try

5oz for $2

You try: The following chart shows how much money Alex earns for mowing lawns. Is the amount of money he earns proportional to the number of hours that he spends mowing?

Earnings ($)

Hours (h)

Unit Rate ( )

14 1

28 2

42 3

56 4

1

$14

2

$28

1

$14

3

$42

1

$14

4

$56

Since the simplified ratios were equal, this was a proportional relationship.

hr

$

1

$14

We typically put time (hours) on the x-axis, and the earnings ($) on the y-axis.

Set up the graph paper to fit the data in the chart.

You try: Let’s graph this proportional relationship from Ex. 1 on an xy-plane.

x

y

Hours worked

Earn

ings

($

)

1

14

28

42

56

2 3 4 5

Hours (h)

Earnings ($)

Point (x, y)

1 14 (1, 14)

2 28 (2, 28)

3 42 (3, 42)

4 56 (4, 56)

Plot points (x, y) from the table.

Connect the points.

Describe the graph of this proportional relationship.

The graph of a proportional relationship:•is a straight line, AND •it passes through the origin, or point (0,0).

Example 2: Ticket Express charges $7 per movie ticket plus a $3 processing fee per order. Is the cost of an order proportional to the number of tickets ordered? Explain .

Cost ($) 10 17 24 31

Tickets Ordered 1 2 3 4

1

$10

ticketsof no.

($)cost 1

$8.5

2

17

1

$8

3

$24

1

$7.75

4

$31

Since all of the simplified ratios are not equal, there is no constant ratio, so this is NOT a proportional relationship.

Tickets ordered will be on the x-axis, and the cost ($) will be on the y-axis.

x

y

Tickets ordered

Cost

($)

1

4

24

32

2 3 4

Tickets Earnings ($) Point (x, y)

0 0 (0,0)

1 10 (1, 10)

2 17 (2, 17)

3 24 (3, 24)

4 31 (4, 31)

Plot points (x, y) from the table.

Connect the points.

Describe the graph of this nonproportional relationship.

Now, let’s graph this nonproportional relationship from Ex. 2.

8

12

16

20

28

It passes through the origin,but it is not a straight line.

Practice:Graphing Worksheet