Moving Straight Ahead - Unit Test Review Sheet

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1 Name: Class: Date: ID: A Moving Straight Ahead - Unit Test Review Sheet Short Answer 1. Brent's Video Shack charges $1.50 to rent a video game for a night. Mr. Buck's Entertainments opens a new store in town, charging $1.00 per night for a game, and starts to take customers away from Brent's Video Shack. a. Graph each price scheme on the same set of axes. b. How could Brent change his charges, so that he includes a one-time membership fee and lowers his rental fee below Mr. Buck's, to get his customers back without losing too much money? Graph your proposal, and explain to Brent how it will work.. Big A's Bike Rentals charges $300 plus $0 per bike to rent bikes for a week. Little Cheeper's rental shop charges $50 plus $35 per bike for a week. You need to determine which company to use for your bike-touring project. Write an explanation to a student who has never used a graphing calculator to help that student display and solve this problem on a graphing calculator. 3. Gretchen was absent when the class developed strategies for solving linear equations. Write an explanation to her about how to solve equations using the symbolic method. Use the equation 4n 17 = 43 as an example. 4. Given one of the representations below, find the other two. Table Graph Equation y = 1 3 x + 1 a. Find the y-intercept for each representation above. b. Find the slope for each representation above. 5. Martin used some rules to generate the following tables: a On grid paper, make a graph of the data in each table. Show the graphs on the same coordinate axes. b. Which sets of data represent a linear relationship? How do you know? 6. a. Find r if r + 10 =. b. Find x if 4.5x = 45. c. Find z if 3z 19 = 173. d. Find w if 67.1 = w. 1

2 Name: ID: A 7. Find the number described in each problem by writing and solving an equation. a. If Sarah subtracts five times her number from 4, she gets 4. What is Sarah's number? b. Twice Bill's number added to 17 is 7. What is Bill's number? c. The sum of 4 times a number and 14 is 16. What is the number? d. If Susan subtracts 11 from one-fourth of her number she gets 11. What is Susan's number? 8. Find x if a. x + 7 = 0 b. 3x + 7 = 0 c. x + 7 = 0 d. How are the solutions similar? How are they different? 9. Find the slope and y-intercept of the line represented by each equation. a. y = x 10 b. y = 4x + 3 c. y = 4x 4.5 d. y =.6x e. y = 7x For each of the lines below, find the slope, and write an equation that represents the line.

3 Name: ID: A 11. Tonya is siphoning all the water from a full aquarium to clean it. The graph below shows the amount of water left in the aquarium as Tonya siphons the water. a. How much water was in the aquarium when it was full? Explain your reasoning. b. How much water does the siphon remove from the aquarium in 1 minute? Explain your reasoning. c. Write an equation that shows the amount of water, G, left in the aquarium after t minutes. d. How many gallons of water are left in the aquarium after 10 minutes? e. How long will it take the siphon to remove all of the water from the aquarium? Explain your reasoning. 1. Line A is the graph of this equation: y = x + Line B is the graph of this equation: y = x a. What is alike about these lines? What is different? b. Write the equation of a line that lies between line A and line B. How is your equation similar to the equations above? How is it different? c. Explain why your equation is correct. 13. Solve each equation to find the value of x. a. 4x + 10 = b. 3x + 9 = 6x c. (x + 3) = 18 d. x + 15 = 7 4x 14. Solve each equation for x. Show your work. a. 3x + 8 = 35 b x = 7x + 3 c. 3(x + 1) = 1 3

4 Name: ID: A Refer to this table, which Francine, Geraldo, and Jennifer made during a bicycling trip. It shows the distance each person traveled during the first four hours of their trip. The table shows the distance covered while the students were actually biking. (Time is not counted when they stop to rest, eat, etc.) Distance (miles) Cycling Time (hours) Francine Geraldo Jennifer a. How fast did each person travel for the first four hours? Explain how you arrived at your answer. b. Assume that each person continued at this rate. Find the distance each person traveled in 6 hours. 16. a. Graph the time and distance for all three people on the same coordinate axes. b. Use the graphs to find the distance each person traveled in.5 hours. c. Use the graphs to find the time it took each person to travel 70 miles. d. How does the rate at which each person rides affect the graphs? 17. a. For each rider, write an equation you can use to calculate the distance traveled after a given number of hours. b. Describe how you could use your equations to calculate the distance each person traveled in.5 hours. c. How does each person's biking rate show up in the equation? 18. a. Stilton was also on the bike trip. The distance he traveled after t hours is represented by d = 7.5t. At what rate of speed was he traveling? b. If you were to put the graph of Stilton's distance and time on the same set of axes as the graphs for Francine, Geraldo, and Jennifer, how would it compare to the other three graphs? 19. Each set of (x, y) coordinates below is generated by a linear rule. For each set of coordinates, write an equation to describe the rule. a. ( 1, 7), (0, -3), (1, 1), (, 5), (4, 13), (5, 17) b. (, 19), ( 1, 14), (0, 9), (, 1), (4, 11), (6, 1) c. (, 1), (0, 3), (1, 5), (3, 9), (5, 13), (6, 15) Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following data sets is linear? A. C. B. D.. What is the equation of the line that contains the points (, 13) and (6, 33)? A. y = 1 5 x + 3 C. y = 1 5 x + 5 B. y = 5x + 5 D. y = 5x + 3 4

5 Name: ID: A Find the slope of the line that passes through the pair of points. 3. (1, 7), (10, 1) 3 A. B. 3 C. 3 D. 3 Solve the equation. 4. x + = 1 A. 0 B. C. 6 D Find the slope of the line. A. 1 B. 1 C. D. 6. Draw a line with a slope of through the point ( 3, 1). A. C. B. D. 7. Determine which ordered pair is a solution of y = 3x + 3. A. (9, ) B. ( 5, 18) C. (1, 6) D. ( 4, 9) 5

6 Name: ID: A 8. Determine which ordered pair is NOT a solution of y = x 7. A. (3, 9) B. ( 4, 3) C. ( 7, 0) D. (4, 11) 9. Identify the slope and y-intercept of y = 1 x + 7. A. 1 ; 7 B. 1 ; 7 C. 1 ; 7 D. 1 ; 7 Graph the linear equation. 10. y = x + A. C. B. D. 6

7 Name: ID: A 11. y = 3 x + 4 A. C. B. D. 1. Find the slope of the line. A. B. 1 C. D. 1 7

8 ID: A Moving Straight Ahead - Unit Test Review Sheet Answer Section SHORT ANSWER 1. ANS: a. b. Possible answer: Brent might charge a membership fee of $5 and then $.50 per game per night. For the first 10 games, Brent's customers will pay more, but after 10 games their total cost will be lower than if they rented from Mr. Buck's. Brent should advertise his plan, emphasizing that if you are a frequent customer you will be better off at Brent's. REF: Moving Straight Ahead Question Bank OBJ: Investigation : Exploring Linear Functions With Graphs and Tables NAT: CC 7.EE.3 CC 7.EE.4 CC 7.EE.4.a NAEP A1b NAEP A1c STA: 7NY 7.A.8 7NY 7.A.10 TOP: Problem.3 Comparing Equations KEY: linear function comparing functions. ANS: On the appropriate screen you need to enter the equations Y 1 = X and Y = X, where X represents the number of bikes. Next you need to set a window appropriate for the context, maybe x values from 0 to 0 and y values corresponding to these, say from 0 to 700. When you graph these equations, you will see two lines giving the costs for the two companies. The point where the lines cross is the point where the two plans cost the same for that number of bikes. Before or after that point, one company or the other has the better deal. REF: Moving Straight Ahead Question Bank STA: 7NY 7.A.8 7NY 7.A.10 TOP: Problem 3.5 Finding the Point of Intersection KEY: solving equations point of intersection 1

9 ID: A 3. ANS: You can think of solving an equation like this one as reversing the procedure that was done to create the expression on the left. To make 4n 17 you would multiply n by 4 and then subtract 17. To reverse this, you add 17, then divide by 4. 4n 17 = 43 4n = n = 60 4n 4 = 60 4 n = 15 REF: Moving Straight Ahead Question Bank STA: 7NY 7.A.8 7NY 7.A.10 TOP: Problem 3.3 Writing Equations KEY: solving equations writing equations 4. ANS: Table Graph Equation y = 3x + 8 y = 4x 3 y = 1 3 x + 1 a. The y-intercepts are 8, 3, and 1. b. The slopes are 3, 4, and 1 3. REF: Moving Straight Ahead Question Bank STA: 7NY 7.A.7 7NY 7.A.8 TOP: Problem 4. Finding the Slope of a Line KEY: slope finding the slope of a line

10 ID: A 5. ANS: a. b. Sets i, ii, and iii represent linear relationships, The graphs of these data sets are straight lines. REF: Moving Straight Ahead Additional Practice Investigation 1 OBJ: Investigation 1: Walking Rates NAT: CC 7.EE.3 CC 7.EE.4 CC 7.EE.4.a NAEP A1a NAEP A1b STA: 7NY 7.A.1 7NY 7.A. 7NY 7.A.3 7NY 7.A.5 TOP: Problem 1.4 Recognizing Linear Relationships KEY: rates linear relationship 6. ANS: a. r = 6 b. x = 10 c. z = 64 d. w = 187 REF: Moving Straight Ahead Additional Practice Investigation 3 STA: 7NY 7.A.8 7NY 7.A.10 TOP: Problem 3.4 Solving Linear Equations KEY: solving equations linear equations 7. ANS: a. 4 5x = 4; 4 b. x + 17 = 7; x = 5 c. 4x + 14 = 16; x = 1 1 d. x 11 = 11; x = 88 4 REF: Moving Straight Ahead Additional Practice Investigation 3 STA: 7NY 7.A.8 7NY 7.A.10 TOP: Problem 3.4 Solving Linear Equations KEY: solving equations linear equations 8. ANS: a. x = 13 b. 3x = 13 so x = 13 3 c. x = 13 so x = 13 d. The numerators of the solutions are all 13; the denominators are the coefficients of x REF: Moving Straight Ahead Additional Practice Investigation 3 STA: 7NY 7.A.8 7NY 7.A.10 TOP: Problem 3.4 Solving Linear Equations KEY: solving equations linear equations 3

11 ID: A 9. ANS: a. slope is ; y-intercept is 10 b. slope is 4; y-intercept is 3 c. slope is 4; y-intercept is 4.5 d. slope is.6; y-intercept is 0 e. slope is 7; y-intercept is 1 REF: Moving Straight Ahead Additional Practice Investigation 4 STA: 7NY 7.A.7 7NY 7.A.8 TOP: Problem 4. Finding the Slope of a Line KEY: slope finding the slope of a line 10. ANS: a. slope is 1; y = x b. slope is 4 3 ; y = 4 3 x c. slope is 3; y = 3x REF: Moving Straight Ahead Additional Practice Investigation 4 STA: 7NY 7.A.7 7NY 7.A.8 TOP: Problem 4.4 Writing Equations with Two Variables KEY: slope equations with two variables 11. ANS: a. 45 gallons; This is the y-intercept (the amount of water in the aquarium at t = 0). 0 b. From the graph, the siphon removes 0 gallons in 1 minutes, or equivalently, 1 = 5 gallons in 1 minute. 3 c. G = 5 3 t + 45 d. Substitute 10 for t in the equation. You get G = 8.33 gallons of water left in the aquarium. e. Substitute 0 for G in the equation. You get t = 7 minutes. REF: Moving Straight Ahead Additional Practice Investigation 4 STA: 7NY 7.A.7 7NY 7.A.8 TOP: Problem 4.4 Writing Equations with Two Variables KEY: slope equations with two variables 1. ANS: a. The slopes are the same; the y-intercepts are different Ê b. y = x + K, where K is any number strictly between and 0; for example, y = x + 1 ˆ ËÁ 3 c. The new line has the same slope so it is parallel to the original two lines; the new constant term is between the original constant terms, so the y-intercept of the new line is between the y-intercept of the original two lines. REF: Moving Straight Ahead Additional Practice Investigation 4 STA: 7NY 7.A.7 7NY 7.A.8 TOP: Problem 4.4 Writing Equations with Two Variables KEY: slope equations with two variables 4

12 ID: A 13. ANS: a. x = 3 b. x = 3 c. x = 6 d. x = REF: Moving Straight Ahead Check Up STA: 7NY 7.A.8 7NY 7.A.10 TOP: Problem 3.4 Solving Linear Equations KEY: solving equations linear equations 14. ANS: a. x = 9 b. x = 4.5 c. x = 3 REF: Moving Straight Ahead Unit Test STA: 7NY 7.A.8 7NY 7.A.10 TOP: Problem 3.4 KEY: solving equations linear equations 15. ANS: a. Francine: 4.5 mph; Geraldo: 6 mph; Jennifer: 7.5 mph; Divide the number of miles traveled in 4 hours by 4. b. Francine: 7 miles; Geraldo: 36 miles; Jennifer: 45 miles REF: Moving Straight Ahead Additional Practice Investigation 1 OBJ: Investigation 1: Walking Rates NAT: CC 7.EE.3 CC 7.EE.4 CC 7.EE.4.a NAEP A1a NAEP A1b STA: 7NY 7.A.1 7NY 7.A. 7NY 7.A.3 7NY 7.A.5 TOP: Problem 1.1 Finding and Using Rates KEY: rates 16. ANS: a. b. Students' estimates should be close to the following values: Francine: 11.5 miles; Geraldo: 15 miles; Jennifer: miles c. Students' estimates should be close to the following values: Francine: 15.6 hours; Geraldo: 11.7 hours; Jennifer: 9.3 hours d. The faster the cyclist, the steeper the graph. REF: Moving Straight Ahead Additional Practice Investigation 1 OBJ: Investigation 1: Walking Rates NAT: CC 7.EE.3 CC 7.EE.4 CC 7.EE.4.a NAEP A1a NAEP A1b STA: 7NY 7.A.1 7NY 7.A. 7NY 7.A.3 7NY 7.A.5 TOP: Problem 1.1 Finding and Using Rates KEY: rates 5

13 ID: A 17. ANS: a. Francine: D = 4.5t; Geraldo: D = 6t; Jennifer: D = 7.5t b. Substitute.5 for t in each equation. c. the number being multiplied by t REF: Moving Straight Ahead Additional Practice Investigation 1 OBJ: Investigation 1: Walking Rates NAT: CC 7.EE.3 CC 7.EE.4 CC 7.EE.4.a NAEP A1a NAEP A1b STA: 7NY 7.A.1 7NY 7.A. 7NY 7.A.3 7NY 7.A.5 TOP: Problem 1. Linear Relationships KEY: rates linear relationship 18. ANS: a. 7.5 miles per hour b. Stilton's graph would be steeper than Francine's and Geraldo's but less steep than Jennifer's. REF: Moving Straight Ahead Additional Practice Investigation 1 OBJ: Investigation 1: Walking Rates NAT: CC 7.EE.3 CC 7.EE.4 CC 7.EE.4.a NAEP A1a NAEP A1b STA: 7NY 7.A.1 7NY 7.A. 7NY 7.A.3 7NY 7.A.5 TOP: Problem 1.3 Using Linear Relationships KEY: rates linear relationship 19. ANS: a. y = 4x 3 b. y = 9 5x c. y = x + 3 REF: Moving Straight Ahead Additional Practice Investigation 1 OBJ: Investigation 1: Walking Rates NAT: CC 7.EE.3 CC 7.EE.4 CC 7.EE.4.a NAEP A1a NAEP A1b STA: 7NY 7.A.1 7NY 7.A. 7NY 7.A.3 7NY 7.A.5 TOP: Problem 1. Linear Relationships KEY: rates linear relationship MULTIPLE CHOICE 1. ANS: B REF: Moving Straight Ahead Multiple Choice OBJ: Investigation 1: Walking Rates NAT: CC 7.EE.3 CC 7.EE.4 CC 7.EE.4.a NAEP A1a NAEP A1b STA: 7NY 7.A.1 7NY 7.A. 7NY 7.A.3 7NY 7.A.5 TOP: Problem 1.4 Recognizing Linear Relationships KEY: rates linear relationship. ANS: D REF: Moving Straight Ahead Multiple Choice STA: 7NY 7.A.7 7NY 7.A.8 TOP: Problem 4.4 Writing Equations with Two Variables KEY: slope equations with two variables 3. ANS: B PTS: 1 DIF: L1 REF: Moving Straight Ahead Skills Practice Investigation 4 STA: 7NY 7.A.7 7NY 7.A.8 TOP: Problem 4. Finding the Slope of a Line KEY: finding slope using points slope 4. ANS: A PTS: 1 DIF: L1 REF: Moving Straight Ahead Skills Practice Investigation 3 STA: 7NY 7.A.8 7NY 7.A.10 TOP: Problem 3.4 Solving Linear Equations KEY: two-step equation algebra 5. ANS: B PTS: 1 DIF: L1 REF: Moving Straight Ahead Skills Practice Investigation 4 STA: 7NY 7.A.7 7NY 7.A.8 TOP: Problem 4. Finding the Slope of a Line KEY: slope rise run slope of a line 6

14 ID: A 6. ANS: C PTS: 1 DIF: L1 REF: Moving Straight Ahead Skills Practice Investigation 4 STA: 7NY 7.A.7 7NY 7.A.8 TOP: Problem 4. Finding the Slope of a Line KEY: slope slope of a line 7. ANS: B PTS: 1 DIF: L1 REF: Moving Straight Ahead Skills Practice Investigation 3 STA: 7NY 7.A.8 7NY 7.A.10 TOP: Problem 3.1 Solving Equations Using Tables and Graphs KEY: solution 8. ANS: A PTS: 1 DIF: L1 REF: Moving Straight Ahead Skills Practice Investigation 3 STA: 7NY 7.A.8 7NY 7.A.10 TOP: Problem 3.1 Solving Equations Using Tables and Graphs KEY: solution 9. ANS: A PTS: 1 DIF: L1 REF: Moving Straight Ahead Skills Practice Investigation OBJ: Investigation : Exploring Linear Functions With Graphs and Tables NAT: CC 7.EE.3 CC 7.EE.4 CC 7.EE.4.a NAEP A1b NAEP A1c STA: 7NY 7.A.8 7NY 7.A.10 TOP: Problem. Using Tables, Graphs, and Equations KEY: y-intercept slope-intercept form 10. ANS: B PTS: 1 DIF: L1 REF: Moving Straight Ahead Skills Practice Investigation 3 STA: 7NY 7.A.8 7NY 7.A.10 TOP: Problem 3.1 Solving Equations Using Tables and Graphs KEY: linear equation graph of an equation with two variables 11. ANS: B PTS: 1 DIF: L1 REF: Moving Straight Ahead Skills Practice Investigation 3 STA: 7NY 7.A.8 7NY 7.A.10 TOP: Problem 3.1 Solving Equations Using Tables and Graphs KEY: linear equation graph of an equation with two variables 1. ANS: C PTS: 1 DIF: L1 REF: Moving Straight Ahead Skills Practice Investigation 4 STA: 7NY 7.A.7 7NY 7.A.8 TOP: Problem 4. Finding the Slope of a Line KEY: slope slope of a line 7