Proportional Relationships

1
Identifying Proportional Relationships From
graphs
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.
2
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
Since the simplified ratios were equal, this was
a proportional relationship.
3
Lets graph this proportional relationship from
Ex. 1 on an xy-plane.
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.
Plot points (x, y) from the table.
y
Hours (h) Earnings () Point (x, y)
1 14 (1, 14)
2 28 (2, 28)
3 42 (3, 42)
4 56 (4, 56)
56
42
Earnings ()
28
14
Connect the points.
x
1
2
3
4
5
Hours worked
Describe the graph of this proportional
relationship.
4

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

5
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

Since all of the simplified ratios are not equal,
there is NOT a proportional relationship between
cost and the number of tickets ordered.
6
Now, lets graph this nonproportional
relationship from Ex. 2.
Tickets ordered will be on the x-axis, and the
cost () will be on the y-axis.
y
Plot points (x, y) from the table.
32
Tickets Earnings () Point (x, y)
1 10 (1, 10)
2 17 (2, 17)
3 24 (3, 24)
4 31 (4, 31)
28
24
Cost ()
20
16
12
8
4
Connect the points.
x
Describe the graph of this nonproportional
relationship.
1
2
3
4
Tickets ordered
7
This graph shows a nonproportional relationship.
It is a straight line, but it does not pass
through the origin.