1. Proportional Relationships
4/21/2017
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. Since the simplified ratios were equal,
4/21/2017
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. 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 ($) on the y-axis.
Set up the graph paper to fit the data in the chart.
Plot points (x, y) from the table. y
Hours (h)
Earnings ($)
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
Describe the graph of this
proportional relationship.
Hours worked

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

5. between cost and the number of tickets ordered.
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, let’s graph this nonproportional relationship from Ex. 2.
Tickets ordered will be on the x-axis,
and the cost ($) will be on the y-axis. y
Plot points (x, y) from the table. 32
Tickets
Earnings ($)
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. nonproportional relationship. It is a straight line, but
This graph shows a
nonproportional relationship.
It is a straight line, but
it does not pass through the origin.