Today, we will graph the information from the tables of values that we worked with yesterday in class.

Our objective is to use a graph to identify if a relationship is proportional or not.

Example 1: 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

$54

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.

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 NOT a proportional relationship

between cost and the number of tickets ordered.

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)

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

This graph shows a nonproportional relationship.

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