5-3 Graphing Proportional Relationships
The table shows how far a
kayak travels down a river
if the kayak is moving at a
rate of 2 miles per hour.
Notice for all ordered pairs in the table for every 1
hour increase in time, the miles traveled increases
by 2. These ordered pairs are in proportion.
y
6
Miles
1= 2 =3 = 4
2
8
4
6
If the ordered pairs are in proportion,
then the data represents a
proportional relationship. When you
graph a proportional relationship, the
result is a line that passes through
the origin.
4
2
0
x
0
2
4
Hours
5-3 Graphing Proportional Relationships
Additional Example 1: Graphing Proportional
Relationships
Graph the linear function y = 4x.
Make a table.
x
y
0
1
2
3
Graph the ordered pairs (0, 0), (1, 4), (2, 8), (3, 12).
5-3 Graphing Proportional Relationships
Additional Example 1 Continued
y
12
10
Place each ordered pair
on the coordinate grid and
then connect the points
with a line.
8
6
4
2
x
0
2
4
Check
6
1 = 2= 3
4
8 12
8
10
The graph is a straight line
that passes through the
origin.
The ordered pairs are proportional.
5-3 Graphing Proportional Relationships
linear equation - an equation whose graph is a
line. The solutions of a linear equation are the
points that make up its graph.
•
Linear equations and linear graphs can be
different representations of linear functions.
linear function - a function whose graph is a
nonvertical line.
5-3 Graphing Proportional Relationships
Some relationships are linear
but not proportional.
The relationships are
proportional if:
•The ordered pairs are
proportional.
•The line passes through the
origin.
5-3 Graphing Proportional Relationships
Additional Example 2A: Identify Proportional
Relationships
Tell whether the function is a proportional
relationship. Then graph the function.
A. y = –2x
Make a table.
x
y
–1
0
1
2
3
The ordered pairs are proportional
and the graph passes through (0, 0).
y = –2x is a proportional
relationship.
5-3 Graphing Proportional Relationships
Additional Example 2B: Identify Proportional
Relationships
Tell whether the function is a proportional
relationship. Then graph the function.
B. y = x – 5
Make a table.
x
y
–1
0
1
2
3
5-3 Graphing Proportional Relationships
Additional Example 3: Earth Science Application
The fastest-moving tectonic plates on Earth
move apart at a rate of 15 centimeters per year.
Write a linear function that describes the
movement of the plates over time. Graph the
relationship. Is this a proportional relationship?
Justify your answer.
Let x represent the input, which is the time in
years. Let y represent the output, which is the
distance in centimeters the plates move apart.
distance in cm = 15 cm/yr  time in years
y
=
15
The function is y = 15x.
▪ x
5-3 Graphing Proportional Relationships
Additional Example 2 Continued
Make a function table. Include a column for the rule.
Input
Rule
Output
x
15(x)
y
0
15(0)
0
1
15(1)
15
2
15(2)
30
3
15(3)
45
Multiply the input by
15.
5-3 Graphing Proportional Relationships
Additional Example 2 Continued
Graph the ordered pairs (0, 0), (1, 15), (2, 30), and
(3, 45) from your table. Connect the points with a line.
y
Centimeters
Check
Use the ordered pairs
100
(1, 15), (2, 30), and
80
(3, 45) to see if the
60
relationship is
proportional.
40
1 = 2 = 3
45
15 30
20
The ordered pairs are
proportional and the graph
0
passes through (0, 0). y = 15x
is a proportional relationship.
2
4
8
Years
10
12
x
5-3 Graphing Proportional Relationships
Lesson Quiz for Student Response Systems
1. Tell whether the linear function y = 2x is a
proportional relationship.
A. yes
B. no
5-3 Graphing Proportional Relationships
Lesson Quiz for Student Response Systems
2. Tell whether the graph of the given linear
function is a proportional relationship.
A. yes
B. no
5-3 Graphing Proportional Relationships
Lesson Quiz for Student Response Systems
3. Larry has 150 cents in his piggy bank. He
puts 20 cents into it everyday. Identify a
linear function that describes the amount
in the piggy bank over time. Is this a
proportional relationship?
A. y = 20x; yes
B. y = –20x; yes
C. y = 150 + 20x; no
D. y = 150 – 20x; no