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

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