5-3 Graphing Proportional Relationships
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
5-3 Graphing Proportional Relationships
Warm Up
Identify the quadrant that contains
each point.
1.(6, –4)
IV
2. (5, 3)
I
3. (–5, –2) III
5-3 Graphing Proportional Relationships
Problem of the Day
Graph the ordered pairs form the table.
What letter do the points form? V
5-3 Graphing Proportional Relationships
Sunshine State Standards
MA.7.A.1.4 Graph proportional
relationships…
5-3 Graphing Proportional Relationships
Vocabulary
linear equation
linear function
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 = 3
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
0
4
8
12
Proportional relationships pass through (0, 0).
Graph the ordered pairs (0, 0), (1, 4), (2, 8), (3, 12).
5-3 Graphing Proportional Relationships
y
12
Additional Example 1 Continued
(3, 12)
10
(1, 4)
Place each ordered pair
on the coordinate grid and
then connect the points
with a line.
(0, 0)
0
2
4
The graph is a straight line
that passes through the
origin.
8
(2, 8)
6
4
2
Check
x
6
1 = 2= 3
4
8 12
8
10
The ordered pairs are proportional.
5-3 Graphing Proportional Relationships
Check It Out: Example 1
Graph y = 15x.
x
0
1
2
3
y
0
15
30
45
y
60
40
20
0
2
4
6
8 x
5-3 Graphing Proportional Relationships
A linear equation is 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. A linear function is a function
whose graph is a nonvertical line.
5-3 Graphing Proportional Relationships
Some relationships are linear
but not proportional. If the
ordered pairs in a linear function
are not all proportional then it is
not a proportional relationship.
These non-proportional
relationships do not pass
through the origin on a graph.
5-3 Graphing Proportional Relationships
Additional Example 2: Identify Proportional
Relationships
Tell whether the function is a proportional
relationship. Then graph the function.
A. y = –2x
Make a table.
x
y
–1
2
0
0
1
–2
2
–4
3
–6
–1 = 1 = 2 = 3
–2
–4 –6
2
The ordered pairs are proportional
and the graph passes through (0, 0).
y = –2x is a proportional
relationship.
5-3 Graphing Proportional Relationships
Check It Out: Example 2
Tell whether y = 10x – 1 is a proportional
relationship. Then graph the function.
x
y
0
–1
1
9
2
19
3
29
4
39
The ordered pairs are not proportional,
and the graph does not pass through (0,
0). y = 10x –1 is not a proportional
relationship.
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

x
The function is y = 15x. Yes, the graph goes
through the origin
5-3 Graphing Proportional Relationships
Additional Example 3 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 3 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
Check It Out: Example 3
The outside temperature is increasing at the
rate of 6 °F per hour. When Reid begins
measuring the temperature, it is 52 °F. Write a
linear function that describes the outside
temperature over time. Graph the relationship.
Is this a proportional relationship? Justify
your answer.
y = 6x + 52, where x is the
number of hours and y is the temperature.
The ordered pairs are not proportional and
the graph does not pass through (0, 0).
y = 6x + 52 is not a proportional relationship.
5-3 Graphing Proportional Relationships
Check it Out: Example 3 Continued
Temperature
100
80
60
40
0
2
4
6
Hours
8
5-3 Graphing Proportional Relationships
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
5-3 Graphing Proportional Relationships
Lesson Quiz: Part I
Tell whether each function is
a proportional relationship.
Then graph the function.
1. y = 3x – 4
no
2. y = –x
yes
3. y = 2x
yes
y = –x
y = 3x – 4
y = 2x
5-3 Graphing Proportional Relationships
Lesson Quiz: Part II
4. The temperature of a liquid is decreasing at a
rate of 12 °F per hour. Susan begins measuring
the liquid at 200 °F. Write a linear function that
describes the change in temperature over time.
Then make a graph to show the temperature
over 5 hours.
y = 200 – 12x; no,
the graph does not
go through the
origin.
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