Transcript Proportional Relationships

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
$
( hr )
1
$14
1
2
$28 $14

2
1
42
3
$42 $14

3
1
56
4
$54 $14

4
1
14
28
Since the simplified ratios were equal,
this was a proportional relationship.
Let’s graph this proportional relationship from Ex. 1 on an xy-plane.
We typically put time (hours) on the x-axis, and
the earnings ($) on the y-axis.
Set up the graph paper to fit the data in the chart.
Plot points (x, y) from the table.
y
Earnings
($)
Point
(x, y)
56
1
14
(1, 14)
42
2
28
(2, 28)
3
42
(3, 42)
4
56
(4, 56)
Connect the points.
Describe the graph of this
proportional relationship.
Earnings ($)
Hours
(h)
28
14
1
2
3
4
Hours worked
5
x
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
cost ($)
no. of tickets
$10
1
17 $8.5

2
1
$24 $8

3
1
$31 $7.75

4
1
Since all of the simplified ratios are not equal, there is
NOT a proportional relationship
between cost and the number of tickets ordered.
Now, let’s graph this nonproportional relationship from Ex. 2.
Tickets ordered will be on the x-axis,
and the cost ($) will be on the y-axis.
y
Plot points (x, y) from the table.
1
2
3
Earnings
($)
10
17
24
Point
(x, y)
28
24
(1, 10)
(2, 17)
(3, 24)
Cost ($)
Ticket
s
32
20
16
12
4
31
(4, 31)
8
Connect the points.
Describe the graph of this
nonproportional relationship.
4
1
2
3
Tickets ordered
4
x
This graph shows a
nonproportional relationship.
It is a straight line, but
it does not pass through the origin.