Lesson 5: Identifying Proportional and Non

Lesson 5
A STORY OF RATIOS
7•1
Lesson 5: Identifying Proportional and Non-Proportional
Relationships in Graphs
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.
𝑥𝑥
Candy Bars Sold
2
4
8
12
𝑦𝑦
Money Received ($)
3
5
9
12
Is the amount of candy bars sold proportional to the money Isaiah received? How do you know?
__________________________________________________________________________________________________
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Example 1: From a Table to Graph
Using the ratio provided, create a table that shows money received is proportional to the number of candy bars sold.
Plot the points in your table on the grid.
14
13
12
𝑥𝑥
𝑦𝑦
11
Candy Bars Sold
Money Received ($)
10
9
2
3
8
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
Lesson 5:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
Identifying Proportional and Non-Proportional Relationships in Graphs
S.17
Lesson 5
A STORY OF RATIOS
7•1
Important Note:
Characteristics of graphs of proportional relationships:
Example 2
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
𝑥𝑥
Candy Bars Sold
𝑦𝑦
Money Received ($)
4
6
2
Money Received, 𝑦𝑦
Graph the points from the Opening Exercise.
3
8
12
12
14
Example 3
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Number of Candy Bars Sold, 𝑥𝑥
Graph the points provided in the table below and describe the similarities and differences when comparing your graph
to the graph in Example 1.
𝑦𝑦
3
9
0
6
6
12
12
18
9
15
Similarities with Example 1:
Differences from Example 1:
Lesson 5:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
20
18
16
14
12
10
8
6
4
2
0
𝑦𝑦
𝑥𝑥
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
𝑥𝑥
Identifying Proportional and Non-Proportional Relationships in Graphs
S.18
7•1
Lesson 5
A STORY OF RATIOS
Lesson Summary
When two proportional quantities are graphed on a coordinate plane, the points appear on a line that passes
through the origin.
Problem Set
Determine whether or not the following graphs represent two quantities that are proportional to each other.
Explain your reasoning.
Donations Matched by Benefactor ($)
a.
b.
Donated Money vs. Donations Matched
by Benefactor
Age vs. Admission Price
8
500
Admission Price ($)
1.
400
300
200
100
0
7
6
5
4
3
2
1
0
0
c.
100
200
300
Money Donated
400
500
0
1
2
3
4
5
6
7
8
Age (years)
Extra Credit Points
Extra Credit vs. Number of Problems
20
18
16
14
12
10
8
6
4
2
0
0
1
2
3
4
5
6
7
8
Number of Problems Solved
Lesson 5:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
Identifying Proportional and Non-Proportional Relationships in Graphs
S.19
2.
7•1
Lesson 5
A STORY OF RATIOS
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.
𝑦𝑦
𝑦𝑦
𝑥𝑥
24
22
20
18
16
14
12
10
8
6
4
2
0
1
2
3
𝑥𝑥
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.
𝑥𝑥
𝑦𝑦
6
6
2
4
3
9
12
1
5
3
3
𝑦𝑦
3.
0
2
4
1
0
𝑥𝑥
𝑦𝑦
2
5
1
4
3
6
4
7
1
2
3
4
5
6
7
8
9 10 11 12
𝑥𝑥
10
9
8
7
6
5
4
3
2
1
0
𝑦𝑦
b.
0
0
1
2
3
4
5
𝑥𝑥
Lesson 5:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
Identifying Proportional and Non-Proportional Relationships in Graphs
S.20