Proportional relationships:
Quantities have a constant ratio, or unit rate
Nonproportional relationships:
Quantities do not have a constant ratio,
or unit rate
Example 1: The following chart shows how much money Layla
earns babysitting. Is the amount of money she earns proportional
to the number of hours that she spends babysitting?
Hours
(h)
Money
earned ($)
1
5.50
2
11.00
3
4
16.50
22.00
Find the unit rate of
money earned to hours
worked for each pair of
values.
money
hours
$5.50
1
$11 $5.50

2
1
$16.50 $5.50

3
1
$22 $5.50

4
1
There is a proportional relationship
between money earned and hours since
all of the ratios have a unit rate of
$5.50
1 hr
.
Let’s graph this proportional relationship from Ex. 1 on an xy-plane.
We typically put time (hours) on the x-axis, and
the money earned ($) on the y-axis.
y
Plot points (x, y) from the table.
Money
Earned ($)
Point
(x, y)
1
5.50
(1, 5.50)
2
11.00
(2, 11)
3
16.50
(3, 16.50)
4
22.00
22.00
Money Earned ($)
Hours
(h)
Layla’s Babysitting Money
16.50
11.00
5.50
(4, 22)
1
The graph of a proportional relationship:
• is a straight line, AND
• it passes through the origin, or point (0,0).
2
3
Hours worked
4
5
x
We can write an equation to represent the proportional
relationship from Ex. 1.
y
Money
Earned ($)
1
5.50
2
11.00
3
16.50
4
22.00
money earned $5.50

hours
1 hr
In words,
22.00
Money Earned ($)
Hours
(h)
Layla’s Babysitting Money
16.50
11.00
5.50
1
2
3
4
5
x
Hours worked
Money earned = (money per hour)(number of hours)
As an equation,
y = $5.50 x
Example 2: Movie World charges a $6 monthly membership fee
plus $1 per movie rental. Is the monthly cost proportional to the
number of movies rented? Explain .
Movies rented
1
2
3
4
Monthly Cost ($)
7
8
9
10
Find the unit rate of the
monthly cost to the number of
rentals for each pair of values.
monthly cost
no. of rentals
$7
 $7
1
8 $4

2 1
$9 $3

3
1
$10 $2.50

4
1
There is NOT a proportional relationship between monthly cost
and number of movie rentals since all of the ratios between the
two quantities are not equal.
Let’s look at a graph this nonproportional relationship from Ex. 2.
Movie rentals will be on the x-axis,
and the monthly cost ($) will be on the y-axis.
y
16
Rentals
Monthly
cost ($)
Point
(x, y)
1
7
(1, 7)
12
2
8
(2, 8)
10
3
9
(3, 9)
4
10
(4, 10)
Monthly Cost of Movies
from Movie World
Cost ($)
14
8
6
4
2
This graph shows a nonproportional
relationship.
 Even though this graph is a straight line,
it does not pass through the origin.
1
2
3
4
Number of movie rentals
x