5.2C Lesson: Proportions from Tables and Graphs*
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1 5.2C Lesson: Proportions from Tables and Graphs* Name: Period: 1. The following table shows the relationship between the amount of cherries (in pounds) and the cost. Cost ($) Amount (lbs.) a. Is this a proportional relationship? How do you know? b. Put the information from the table on the graph below, with pounds of cherries on the x-axis and cost on the y-axis. Draw a straight line through the points if you can. c. Examine the graph. What conclusions can you make? d. Is the weight dependent on the cost, or is the cost dependent on the weight? Explain. SDUHSD Math A Honors Module #5 STUDENT EDITION 36
2 2. The following table shows the relationship between the ounces of soup and the cost. Cost ($) Amount (oz) a. Is this a proportional relationship? How do you know? b. Graph the information in the table, using the x-axis for amount (oz) and y-axis for the cost. Draw a straight line through the points if you can. c. Examine the graph. What conclusions can you make? d. State the independent and dependent variables. This means that one variable depends on the other variable. 3. The following table shows the pounds of meat on a sandwich and the calories in the sandwich. Calories Meat (lbs) a. Is this a proportional relationship? How do you know? b. Graph the information from the table, using the x-axis for meat (lbs) and y-axis for calories. c. Examine the graph. What conclusions can you make? d. State the independent and dependent variables. SDUHSD Math A Honors Module #5 STUDENT EDITION 37
3 4. Bubba s Body Shop charges $25 per hour to fix a car. Complete the table and graph to represent this situation. Be sure to label the axes of your graph. Draw a straight line through the points if you can. Time in Hours t 0 Cost in Dollars: c a. Are cost and time proportionally related in this situation? How do you know? b. Examine the graph. What conclusions can you make? c. State the independent and dependent variables. 5. Sunset Splash and Spa charges an entrance fee of $5.00 and then $2.00 per hour. Complete the table and graph to represent this situation. Be sure to label the axes of your graph. Draw a straight line through the points if you can. Time in Hours t 0 Cost in Dollars: c a. Are cost and time proportionally related in this situation? How do you know? b. Examine the graph. What conclusions can you make? c. State the independent and dependent variables. SDUHSD Math A Honors Module #5 STUDENT EDITION 38
4 6. Complete the graph for the table below. Be sure to label your axes. Draw a straight line through the points if you can. # of MP3s Price ($) a. Are number of MP3s and price proportionally related in this situation? How do you know? b. Examine the graph. What conclusions can you make? c. State the independent and dependent variables. In math, we often make conjectures after observing something. For example, if you observe that your math teacher wore a geeky math t-shirt every day for the first week of school, you might make a conjecture that your math teacher will wear geeky t-shirts the second week of school. A conjecture is a conclusion based on observations, similar to an educated guess that you have to justify. 7. Make a conjecture about how to determine if a table of values represents a proportional relationship. 8. Make a conjecture about how to determine if a graph of values represents a proportional relationship. When two quantities are proportionally related, their unit rate is the same throughout the table, or constant. This rate is also called the constant of proportionality, or the proportional constant. SDUHSD Math A Honors Module #5 STUDENT EDITION 39
5 9. Peter is renting Wave Runners for a company party. Each Wave Runner holds 3 people. a. Complete the table below to show the relationship between the number of Wave Runners rented and the number of people that can ride. b. Graph this relationship. Have the number of Wave Runners be on the x-axis and the number of riders be on the y-axis. Label the axes and draw a straight line through the points if you can.. Number of Wave Runners 0 Number of Riders c. Find the ratio of number of riders to number of Wave Runners for several different ordered pairs in the table. number of riders number of Wave Runners d. Where do you see the unit rate in the table? e. Describe (0,0) in the context of the problem. f. Does the situation represent a proportional relationship? Justify your answer using the table of values and graph. Table of values:. Graph: g. If the relationship is proportional, state the constant of proportionality. (Hint: Refer to the definition on the previous page.) h. Use the relationship and graph to determine how many Wave Runners Peter needs to rent if there will be 21 people at his company party that all want to ride a Wave Runner. i. What is the relationship between the number of riders and the number of Wave Runners? j. Can you use this relationship to determine how many Wave Runners Peter needs to rent if there will be 21 people at his company party that all want to ride a Wave Runner? How? SDUHSD Math A Honors Module #5 STUDENT EDITION 40
6 In the last problem, the number of riders, r, is proportionally related to the number of Wave Runners, w. The equation that represents this relation is 3, where r relates to w through multiplication. 10. A dog runs 3 meters every second. Complete the table and graph to represent this situation. Be sure to label the axes of your graph. Draw a straight line through the points if you can. Time (seconds) t 0 Distance (meters) d a. What is the unit rate for this problem, if there is one? b. If a dog runs for 45 seconds, how far will the dog go? c. Write an equation to show the relationship between the distance the dog travels, d, for t, time in seconds. d. What is the constant of proportionality? e. Are distance and time proportionally related in this situation? Justify your answer using your table, graph, and equation. Table: Graph: Equation: SDUHSD Math A Honors Module #5 STUDENT EDITION 41
7 11. Identify if the following graphs are proportional, and justify your reasoning. If proportional, identify the constant of proportionality. If not proportional, write none. a. b. i. Is this a proportional relationship? Explain. i. Is this a proportional relationship? Explain. ii. If proportional, estimate the constant of proportionality: ii. If proportional, estimate the constant of proportionality: c. d. i. Is this a proportional relationship? Explain. i. Is this a proportional relationship? Explain. ii. If proportional, estimate the constant of proportionality: ii. If proportional, estimate the constant of proportionality: 12. For the two scenarios below, complete the table and determine if it shows a proportional relationship. If it is proportional, state the proportional constant. a. A flower that is 3 inches tall when planted and grows ½ an inch every 4 weeks. Weeks Height (in) Is it proportional? If so, what is the proportional constant? b. The sum of two non-zero numbers is 0. Use x and y to represent the two numbers Is it proportional? If so, what is the proportional constant? SDUHSD Math A Honors Module #5 STUDENT EDITION 42
8 For #13-15, decide whether you think the relationship described is proportional or not proportional and justify your reasoning. If the relationship is proportional, state the independent and dependent variables. 13. Carlos wants to buy some new video games. Each game he buys costs him $36. Is the relationship between the number of games Carlos buys and the total price proportional? 14. A single ticket to a concert costs $56, while buying five tickets costs $250. Is the relationship between the number of tickets bought and the total price proportional? 15. Anna has a new video game. It takes her five hours of playing the game to master Level One. After so much time, Anna understands the game better and it only takes her three hours of playing the game to master Level Two. Is the number of hours played and the game level proportional? SDUHSD Math A Honors Module #5 STUDENT EDITION 43
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This is a function because no vertical line can be drawn so that it intersects the graph more than once.
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