Name: ______________________________________ Date: ____________ Period: __________
Lesson 5: Identifying Proportional and Non-Proportional
Relationships in Graphs
Student Outcomes

Students decide whether two quantities are proportional to each other by graphing on a coordinate
plane and observing whether the graph is a straight line through the origin.

Students study examples of quantities that are proportional to each other as well as those that are not.
Classwork
Opening Exercise
Isaiah sold candy bars to help raise money for his scouting troop. The table shows the amount of candy he sold
compared to the money he received.
𝒙
Candy Bars Sold
2
4
8
12
𝒚
Money Received ($)
3
5
9
12
Is the amount of candy bars sold proportional to the money Isaiah received? How do you know?
_____________________________________________________________________________________________
_____________________________________________________________________________________________
Exploratory Challenge: From a Table to a Graph
Using the ratio provided, create a table that shows money received is proportional to the number of candy bars
sold. Plot the points in your table on the grid.
14
13
𝒙
𝒚
12
Candy Bars Sold
Money Received ($)
11
10
2
3
9
8
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
Example 1
𝒙
Candy Bars Sold
𝒚
Money Received ($)
2
3
4
5
8
9
12
12
Money Received, 𝑦
Graph the points from the Opening Exercise.
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Number of Candy Bars Sold, 𝑥
Example 2
Graph the points provided in the table below, and describe the similarities and differences when comparing your
graph to the graph in Example 1.
20
𝒙
𝒚
0
6
3
9
14
6
12
12
9
15
10
12
18
Similarities with Example 1:
18
𝑦
16
8
6
4
2
0
0
Differences from Example 1:
1
2
3
4
5
6
7
𝑥
8
9 10 11 12 13 14
Lesson Summary
When two proportional quantities are graphed on a coordinate plane, the points appear on a line that passes
through the origin.
Problem Set
Determine whether or not the following graphs represent two quantities that are proportional to each other.
Explain your reasoning.
b.
Age vs. Admission Price
Donated Money vs. Donations Matched
by Benefactor
8
500
Admission Price ($)
Donations Matched by Benefactor ($)
a.
400
300
200
7
6
5
4
3
2
100
1
0
0
0
100
200
300
400
0
500
Money Donated
Extra Credit vs. Number of Problems
20
18
16
14
12
10
8
6
4
2
0
0
1
2
3
4
1
2
3
4
5
Age (years)
c.
Extra Credit Points
1.
5
6
Number of Problems Solved
7
8
6
7
8
2.
Create a table and a graph for the ratios 2: 22, 3 to 15, and 1: 11. Does the graph show that the two
quantities are proportional to each other? Explain why or why not.
𝒚
𝑦
𝒙
24
22
20
18
16
14
12
10
8
6
4
2
0
0
3.
1
2
3
𝑥
4
5
Graph the following tables, and identify if the two quantities are proportional to each other on the graph.
Explain why or why not.
a.
6
𝒚
5
3
1
4
6
2
3
9
3
2
12
4
1
𝑦
𝒙
0
0
b.
1
2
3
4
5
6
7
8
9 10 11 12
𝒙
𝒚
1
4
2
5
3
6
4
7
𝑦
𝑥
10
9
8
7
6
5
4
3
2
1
0
0
1
2
3
𝑥
4
5
Exit Ticket
1.
The following table gives the number of people picking strawberries in a field and the corresponding number
of hours that those people worked picking strawberries. Graph the ordered pairs from the table. Does the
graph represent two quantities that are proportional to each other? Explain why or why not.
10
𝒙
𝒚
9
1
3
8
7
1
6
4
2
5
𝑦
7
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
10
𝑥
Use the given values to complete the table. Create quantities proportional to each other and graph them.
10
𝒙
9
𝒚
8
7
4
2
6
𝑦
2.
5
4
3
2
1
0
0
1
2
3
4
5
𝑥
6
7
8
9
10
3.
a.
What are the differences between the graphs in Problems 1 and 2?
a.
What are the similarities in the graphs in Problems 1 and 2?
b.
What makes one graph represent quantities that are proportional to each other and one graph not
represent quantities that are proportional to each other in Problems 1 and 2?