Lesson 2.1 Assignment Name Date What Makes You Tap Your Feet? Introduction to Direct Variation 1. In 2010, Chevrolet produced 12,194 Corvettes. That means they made Corvettes at a rate of about 34 cars per day. a. How many Corvettes did Chevrolet produce in 7 days? Show your work. b. How many days did it take Chevrolet to produce 1190 Corvettes? Show your work. c. Complete the table. Time (days) Number of Corvettes 7 21 1 2 1190 952 Chapter 2 Assignments 27
Lesson 2.1 Assignment page 2 d. Use the data in the table to complete the graph. y Corvette Production Number of Corvettes 1080 960 840 720 600 480 360 240 120 4 8 12 16 20 24 28 32 36 Time (days) x e. Is the data in the graph discrete or continuous? Explain your reasoning. f. Does it make sense to connect the points in this graph? If so, connect them. Explain your reasoning. g. What is the ratio of Corvette production to time? h. Does the number of Corvettes vary directly with time? Explain your reasoning. 28 Chapter 2 Assignments
Lesson 2.2 Assignment Name Date Building Bird Feeders Is for the Birds! Determining Equivalent Ratios The student council at Camp Creek Middle School determine that 3 out of 4 students prefer that all school assemblies be held on Friday afternoon. 1. If 200 students are surveyed, how many will prefer that school assemblies be held on Friday afternoon? Explain how you determined your answer. 2. If 747 students prefer that school assemblies be held on Friday afternoon, how many students were surveyed? Explain how you determined your answer. Chapter 2 Assignments 29
Lesson 2.2 Assignment page 2 Analyze each table shown. Determine if the relationship is proportional. If the relationship is proportional, calculate the equivalent ratio to justify your answer. 3. Of the 75 boys in the 7th grade class, 25 participate in at least one sport. Of the 120 girls in the 7th grade class, 30 participate in at least one sport. 7th Grade Class Plays Sports Total Boys 25 75 Girls 30 120 4. Of the 210 boys in the 8th grade, 190 have a cell phone. Of the 168 girls in the 8th grade, 152 have a cell phone. 8th Grade Class Cell Phones Total Boys 190 210 Girls 152 168 30 Chapter 2 Assignments
Lesson 2.2 Assignment page 3 Name Date 5. Of the 250 sixth graders, 75 said they went to the movies over the weekend. Of the 180 seventh graders, 54 said they went to the movies over the weekend. Of the 200 eighth graders, 65 said they went to the movies over the weekend. Class Attended a Movie Total 6th Graders 75 250 7th Graders 54 180 8th Graders 65 200 6. In the town of Clover, 3 out of 5 citizens who are eligible to vote did so in the spring election. a. Write an equation showing the relationship between the citizens who voted (v) and the citizens who are eligible to vote (e) and the equivalent ratio. b. Use the equation from part (a) to determine the number of citizens that voted in the spring election if 400 citizens were eligible to vote. Chapter 2 Assignments 31
Lesson 2.2 Assignment page 4 c. Use the equation from part (a) to determine the number of citizens that were eligible to vote in the spring election if 180 actually voted. 32 Chapter 2 Assignments
Lesson 2.3 Assignment Name Date Kids Just Wanna Have Fun! Determining and Applying the Constant of Proportionality 1. Shilo is riding her bicycle across the state of Georgia to raise money for her favorite charity. The distance (d ) in miles that she can travel varies directly with the length of time (t) in hours she spends riding. Assume that her constant of proportionality is 18. a. Write an equation showing the proportional relationship between d and t using the information given. b. If Shilo rides for 3 hours, how far will she travel? Use your equation to show the relationship between distance and time. c. How long does it take Shilo to ride 6 miles? Use your equation to show the relationship between distance and time. Chapter 2 Assignments 33
Lesson 2.3 Assignment page 2 d. What does the constant of proportionality represent in this problem? 2. Maya s construction company builds brick houses. The table shows the relationship between the time Maya works and the number of bricks she can install. Hours Worked Bricks Installed 8 1680 7 1470 6 1260 a. Define variables for the quantities that are changing in this problem situation. b. Analyze the table to determine if the relationship is proportional. Explain your reasoning and state a constant of proportionality if possible. c. What does the constant of proportionality represent in this problem? d. Write an equation showing the relationship between the number of hours worked, the number of bricks installed, and the constant of proportionality. 34 Chapter 2 Assignments
Lesson 2.3 Assignment page 3 Name Date e. Use your equation from part (d) to determine how many bricks Maya can install in 5.5 hours. Show your work. f. Use your equation from part (d) to determine how many hours it will take Maya to install 840 bricks. Show your work. Chapter 2 Assignments 35
Lesson 2.3 Assignment page 4 Solve each using the equation for the constant of proportionality, y x 5 k. 3. k 5 2 and x 5 21 4. k 5 0.3 and y 5 18 7 36 Chapter 2 Assignments
Lesson 2.4 Assignment Name Date Stop that Speeding Snail? Using the Constant of Proportionality to Solve Proportions 1. Dudley and Bob monitored the distance their pet turtle could walk in a certain amount of time. Their results are shown in the table. The table of values represents a proportional relationship. Time (minutes) Distance (inches) 5 14.5 14 40.8 19 55.1 25 72.5 a. Define variables for the quantities that are changing in this problem situation. b. How can you determine the constant of proportionality using the values in the table? c. What is the constant of proportionality? Chapter 2 Assignments 37
Lesson 2.4 Assignment page 2 2. Analyze each table or problem situation to determine if the relationship is proportional. State a constant of proportionality if possible. Show your work. a. Girls Boys 7 14 9 21 11 22 b. A baby blue whale weighed 5520 pounds at birth. After two days, the baby weighed 5710. After 14 days, the baby weighed 8180 pounds. Is there a constant of proportionality? 38 Chapter 2 Assignments
Lesson 2.5 Assignment Name Date The Man Who Ran from Marathon to Athens Graphing Direct Proportions 1. Tony is going into sixth grade in the fall. During the summer, he is required to read at least two books from an approved reading list and to complete a mini-project to accompany each book. Suppose the number of pages ( p) that Tony can read varies directly with the amount of time (t) in hours he spends reading. Suppose the constant of proportionality relating the variables p and t is 30. a. Write an equation showing the relationship between the number of pages read and the time spent reading. Assume that Tony always maintains the same rate of reading. b. What does the constant of proportionality represent in this problem? c. Complete the table showing the amount of time spent reading and the number of pages read using your equation from part (a). Time (in hours) t Number of Pages Read p 0.5 37.5 2.5 3 60 Chapter 2 Assignments 39
Lesson 2.5 Assignment page 2 d. Graph the values in the table from part (c) on the coordinate plane shown. Graph the values of t on the x-axis and the values of p on the y-axis. p 90 80 Number of Pages Read 70 60 50 40 30 20 10 1 2 3 4 Time (in hours) t e. Explain how the graph verifies that the number of pages Tony reads is directly proportional to the amount of time he spends reading. f. Interpret the meaning of the point (2.5, 75) on the graph. 40 Chapter 2 Assignments
Lesson 2.5 Assignment page 3 Name Date g. For each of the following points on the graph, form the ratio y-coordinate in the table. x-coordinate Then, simplify the ratio. What do you notice? What is significant about what you noticed? x-coordinate y-coordinate y-coordinate x-coordinate 0.5 37.5 60 2.5 3 2. Mariah is trying to improve her math skills over the summer. When she reads her math book, the number of pages she can read depends on the difficulty of the concept being studied. Mariah keeps track of the amount of time and the number of pages read during several study sessions in the table. Time (in hours) Number of Pages Read 0.5 5 0.75 7 1 10 1.5 8 2 12 Chapter 2 Assignments 41
Lesson 2.5 Assignment page 4 a. Graph each point from the table on the graph shown. Label the x- and y-axis and name your graph. 18 16 14 12 10 8 6 4 2 1 2 3 4 b. What do you notice about the points you plotted? c. Determine if there is a constant of proportionality. Pick two points from the graph to form the ratio y-coordinate x-coordinate. 42 Chapter 2 Assignments
Lesson 2.6 Assignment Name Date Racing to the Finish Line! Using Direct Proportions 1. Jameer works in a men s clothing store. The amount of money (m) he makes is directly proportional to the number of hours (h) he works. a. Complete the table to show the amount of money Jameer earns for the different amounts of time that he works. Hours (h) Money (m) (in dollars) 3 56.25 6 75.00 7.5 b. Determine the constant of proportionality and interpret it in the context of the problem. c. Write an equation showing the relationship between m and h. d. How many hours does Jameer have to work to make $100? Chapter 2 Assignments 43
Lesson 2.6 Assignment page 2 e. How much money does Jameer earn if he works 40 hours? 2. Henry knows that whenever he buys something he is charged a sales tax. This sales tax (t) varies directly with the amount of money (m) he spends on the item. a. Write an equation representing the direct proportional relationship between the sales tax and the amount of money spent. Use the variable k as the constant of proportionality. b. If Henry pays $1.76 in sales tax on an item that costs $22, what is the value of the constant of proportionality? c. What does the constant of proportionality represent in this problem? 44 Chapter 2 Assignments
Lesson 2.6 Assignment page 3 Name Date d. If Henry buys an item that costs $76, how much is the sales tax? Use the constant of proportionality you calculated in part (b). e. How much does an item cost if the sales tax is $1.04? Use the constant of proportionality you calculated in part (b). Chapter 2 Assignments 45
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Lesson 2.7 Assignment Connecting Representations of Proportional Relationships Interpreting Multiple Representations of Direct Proportions 1. Millie is cutting out stars to decorate the gym for the school dance. The number of stars (s) she can cut out varies directly with the time (t) in minutes she spends cutting out the stars. a. Write an equation showing the relationship between s and t. b. Complete the table to show the number of stars Millie is able to cut out for various amounts of time. Explain how you completed the table. Time (t) (in minutes) Number of Stars (s) s t 5 k 0 ------ 12 6 15 44 50 Chapter 2 Assignments 47
Lesson 2.7 Assignment page 2 c. Write the equation representing the relationship between s and t using the value of k you determined from the table. d. Graph the data. Label the x- and y-axes and name your graph. e. Did the graph turn out as you expected? Explain. f. Determine the constant of proportionality in two different ways by using the graph. 48 Chapter 2 Assignments