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. Use the graph at the right. a. Find the slope of the line. b. Find the equation of the line. 2. Does the table below represent a linear relationship? If so, write an equation for that relationship. If not, explain. Time (s) Distance (m) Solve each equation for x. Show your work. a. 3x + 8 = 35 b x = 7x + 3 c. 3(x + 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. 5. Big A's Bike Rentals charges $300 plus $20 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. 1

2 Name: ID: A 6. 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. 7. 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. 8. 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? 2

3 Name: ID: A 9. The equations below represent the distances in meters traveled after t seconds by three cyclists. a. For which equation does the point (10, 74) lie on the graph? Explain. i. D = 2.4t + 32 ii. D = 4.2t + 32 iii. D = 6t + 32 b. For each equation, give the coordinates of a point on the graph of the equation. 10. a. Find r if 2r + 10 = 22. b. Find x if 4.5x = 45. c. Find z if 3z 19 = 173. d. Find w if 67.1 = w. 11. Find the number described in each problem by writing and solving an equation. a. If Sarah subtracts five times her number from 24, 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? 12. Find x if a. x + 7 = 20 b. 3x + 7 = 20 c. 2x + 7 = 20 d. How are the solutions similar? How are they different? 13. Find the slope and y-intercept of the line represented by each equation. a. y = 2x 10 b. y = 4x + 3 c. y = 4x 4.5 d. y = 2.6x e. y = 7x + 1 3

4 Name: ID: A 14. For each of the lines below, find the slope, and write an equation that represents the line. 4

5 Name: ID: A 15. 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. 16. Line A is the graph of this equation: y = 2x + 2 Line B is the graph of this equation: y = 2x 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. 5

6 Name: ID: A 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. 2. Which of the following is linear? A. y = 2 + 3x B. y = 2x(x + 5) C. y = 4x 2 D. y = 2 x Use the following table to answer questipns 3-5. X Y What is the slope of data set? A. 4 B. 3 C. 1 D What is the y-intercept of the data set? A. 4 B. 3 C. 1 D What is the equation to represent the data set? A. y = x + 3 C. y = 3x + 1 B. y = 4x + 1 D. y = 3x Consider the equation y = 4x 10. Find y if x = 3. A. 33 B. 12 C. 2 D What is the equation of the line that contains the points (2, 13) and (6, 33)? A. y = 1 5 x + 3 C. y = 1 5 x + 5 B. y = 5x + 5 D. y = 5x + 3 6

7 Name: ID: A Find the slope of the line that passes through the pair of points. 8. (1, 7), (10, 1) 3 A. 2 B. 2 3 C. 3 2 D ( 5.5, 6.1), ( 2.5, 3.1) A. 1 B. 1 C. 1 D A student finds the slope of the line between (14, 1) and (18, 17). She writes What mistake did she make? A. She should have added the values, not subtracted them. B. She used y-values where she should have used x-values. C. She mixed up the x- and y-values. D. She did not keep the order of the points the same in numerator and the denominator. Write an equation in point-slope form for the line through the given point with the given slope. 11. (10, 9); m = 2 A. y 10 = 2(x + 9) C. y 9 = 2(x 10) B. y 9 = 2(x + 10) D. y + 9 = 2(x 10) Solve the equation. 12. x = 12 A. 20 B. 22 C. 26 D The science club is selling puzzles to raise money. The supplier charges a one-time fee of $55 for each order and $10 for each puzzle. Write and solve an equation to find the number of puzzles the science club can buy if they have $1,245. A p = 1,245; 119 puzzles C. 10p 55 = 1,245; 23 puzzles B. 65p = 1,245; 20 puzzles D. 1,245 = 10p + 55; 130 puzzles 7

8 Name: ID: A 14. Graph the points A(5, 4 ), B(1, 2), and C(3, 3) on the same coordinate plane. A. C. B. D. 8

9 Name: ID: A Graph the linear equation. 15. y = 3x 4 A. C. B. D. 9

10 Name: ID: A 16. y = 1 5 x + 4 A. C. B. D. 17. Find the slope of the line. A. 1 2 B. 1 2 C. 2 D. 2 10

11 Name: ID: A 18. Draw a line with a slope of 2 through the point ( 3, 1). A. C. B. D. 19. Determine which ordered pair is a solution of y = 3x + 3. A. (9, 2) B. ( 5, 18) C. (1, 6) D. ( 4, 9) 20. Determine which ordered pair is NOT a solution of y = x 7. A. (3, 9) B. ( 4, 3) C. ( 7, 0) D. (4, 11) 21. Identify the slope and y-intercept of y = 1 2 x + 7. A. 1 2 ; 7 B. 1 2 ; 7 C. 1 2 ; 7 D. 1 2 ; 7 11

12 ID: A Moving Straight Ahead - Unit Test Review Sheet Answer Section SHORT ANSWER 1. ANS: a. The slope is 3. Encourage students to check several points on the line. For example, the slope using (0, 2) and (1, 1) is 3, as is the slope between (1, 1) and (2, 4). b. y = 3x 2 PTS: 1 DIF: L2 REF: Moving Straight Ahead Unit Test STA: 7NY 7.A.7 7NY 7.A.8 TOP: Problem 4.2 KEY: slope equations with two variables 2. ANS: Yes. The equation is y = 2x PTS: 1 DIF: L2 REF: Moving Straight Ahead Unit Test OBJ: Investigation 2: Exploring Linear Functions With Graphs and Tables NAT: CC 7.EE.B.3 CC 7.EE.B.4 CC 7.EE.B.4a CC 7.RP.A.2b CC 7.RP.A.2c CC 7.RP.A.2d TOP: Problem ANS: a. x = 9 b. x = 4.5 c. x = 3 PTS: 1 DIF: L2 REF: Moving Straight Ahead Unit Test STA: 7NY 7.A.8 7NY 7.A.10 TOP: Problem 3.4 KEY: solving equations linear equations 1

13 ID: A 4. 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. PTS: 1 DIF: L2 REF: Moving Straight Ahead Question Bank OBJ: Investigation 2: 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 2.3 Comparing Equations KEY: linear function comparing functions 5. ANS: On the appropriate screen you need to enter the equations Y 1 = X and Y 2 = 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 20 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. PTS: 1 DIF: L2 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 2

14 ID: A 6. 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 PTS: 1 DIF: L2 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 3

15 ID: A 7. 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. PTS: 1 DIF: L2 REF: Moving Straight Ahead Question Bank STA: 7NY 7.A.7 7NY 7.A.8 TOP: Problem 4.2 Finding the Slope of a Line KEY: slope finding the slope of a line 4

16 ID: A 8. ANS: a. b. Sets i, ii, and iii represent linear relationships, The graphs of these data sets are straight lines. PTS: 1 DIF: L2 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.2 7NY 7.A.3 7NY 7.A.5 TOP: Problem 1.4 Recognizing Linear Relationships KEY: rates linear relationship 9. ANS: a. Equation ii because the point satisfies the equation: 74 = 4.2(10) b. Answers will vary. PTS: 1 DIF: L2 REF: Moving Straight Ahead Additional Practice Investigation 3 STA: 7NY 7.A.8 7NY 7.A.10 TOP: Problem 3.1 Solving Equations Using Tables and Graphs KEY: solving equations tables and graphs 10. ANS: a. r = 6 b. x = 10 c. z = 64 d. w = 187 PTS: 1 DIF: L2 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 5

17 ID: A 11. ANS: a. 24 5x = 4; 4 b. 2x + 17 = 7; x = 5 c. 4x + 14 = 16; x = 1 1 d. x 11 = 11; x = PTS: 1 DIF: L2 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 12. ANS: a. x = 13 b. 3x = 13 so x = 13 3 c. 2x = 13 so x = 13 2 d. The numerators of the solutions are all 13; the denominators are the coefficients of x PTS: 1 DIF: L2 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 13. ANS: a. slope is 2; y-intercept is 10 b. slope is 4; y-intercept is 3 c. slope is 4; y-intercept is 4.5 d. slope is 2.6; y-intercept is 0 e. slope is 7; y-intercept is 1 PTS: 1 DIF: L2 REF: Moving Straight Ahead Additional Practice Investigation 4 STA: 7NY 7.A.7 7NY 7.A.8 TOP: Problem 4.2 Finding the Slope of a Line KEY: slope finding the slope of a line 6

18 ID: A 14. ANS: a. slope is 1; y = x b. slope is 4 3 ; y = 4 3 x c. slope is 3; y = 3x PTS: 1 DIF: L2 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 15. ANS: a. 45 gallons; This is the y-intercept (the amount of water in the aquarium at t = 0). b. From the graph, the siphon removes 20 gallons in 12 minutes, or equivalently, minute. c. G = 5 3 t = 5 3 d. Substitute 10 for t in the equation. You get G = gallons of water left in the aquarium. e. Substitute 0 for G in the equation. You get t = 27 minutes. gallons in 1 PTS: 1 DIF: L2 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 16. ANS: a. The slopes are the same; the y-intercepts are different Ê b. y = 2x + K, where K is any number strictly between 2 and 0; for example, y = 2x + 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. PTS: 1 DIF: L2 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 7

19 ID: A MULTIPLE CHOICE 1. ANS: B PTS: 1 DIF: L2 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.2 7NY 7.A.3 7NY 7.A.5 TOP: Problem 1.4 Recognizing Linear Relationships KEY: rates linear relationship 2. ANS: A PTS: 1 DIF: L2 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.2 7NY 7.A.3 7NY 7.A.5 TOP: Problem 1.4 Recognizing Linear Relationships KEY: rates linear relationship 3. ANS: B PTS: 1 DIF: L2 REF: Moving Straight Ahead Multiple Choice STA: 7NY 7.A.7 7NY 7.A.8 TOP: Problem 4.2 Finding the Slope of a Line KEY: slope finding the slope of a line 4. ANS: C PTS: 1 DIF: L2 REF: Moving Straight Ahead Multiple Choice OBJ: Investigation 2: 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 2.3 Comparing Equations KEY: linear function comparing functions 5. ANS: C PTS: 1 DIF: L2 REF: Moving Straight Ahead Multiple Choice STA: 7NY 7.A.8 7NY 7.A.10 TOP: Problem 3.3 Writing Equations KEY: solving equations writing equations 6. ANS: C PTS: 1 DIF: L2 REF: Moving Straight Ahead Multiple Choice STA: 7NY 7.A.8 7NY 7.A.10 TOP: Problem 3.4 Solving Linear Equations KEY: solving equations linear equations 7. ANS: D PTS: 1 DIF: L2 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 8. 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 4.2 Finding the Slope of a Line KEY: finding slope using points slope 8

20 ID: A 9. ANS: A PTS: 1 DIF: L2 REF: Moving Straight Ahead Skills Practice Investigation 4 STA: 7NY 7.A.7 7NY 7.A.8 TOP: Problem 4.2 Finding the Slope of a Line KEY: finding slope using points slope 10. ANS: D PTS: 1 DIF: L2 REF: Moving Straight Ahead Skills Practice Investigation 4 STA: 7NY 7.A.7 7NY 7.A.8 TOP: Problem 4.2 Finding the Slope of a Line KEY: slope reasoning error analysis 11. ANS: D PTS: 1 DIF: L1 REF: Moving Straight Ahead Skills Practice Investigation 4 STA: 7NY 7.A.7 7NY 7.A.8 TOP: Problem 4.3 Exploring Patterns With Lines KEY: slope-intercept form linear equation 12. 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 13. ANS: A PTS: 1 DIF: L1 REF: Moving Straight Ahead Skills 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.2 7NY 7.A.3 7NY 7.A.5 TOP: Problem 1.2 Linear Relationships KEY: write an equation word problem problem solving multi-part question algebra two-step equation 14. ANS: C PTS: 1 DIF: L1 REF: Moving Straight Ahead Skills 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.2 7NY 7.A.3 7NY 7.A.5 TOP: Problem 1.2 Linear Relationships KEY: quadrants ordered pair coordinates x-axis x-coordinate y-axis y-coordinate origin graphing a point 15. ANS: A PTS: 1 DIF: L1 REF: Moving Straight Ahead Skills 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.2 7NY 7.A.3 7NY 7.A.5 TOP: Problem 1.2 Linear Relationships KEY: graph of an equation linear equation graphing a linear equation ordered pair algebra 9

21 ID: A 16. ANS: A PTS: 1 DIF: L2 REF: Moving Straight Ahead Skills 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.2 7NY 7.A.3 7NY 7.A.5 TOP: Problem 1.2 Linear Relationships KEY: graph of an equation linear equation graphing a linear equation ordered pair algebra 17. 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 4.2 Finding the Slope of a Line KEY: slope rise run slope of a line 18. 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 4.2 Finding the Slope of a Line KEY: slope slope of a line 19. 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 20. 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 21. ANS: A PTS: 1 DIF: L1 REF: Moving Straight Ahead Skills Practice Investigation 2 OBJ: Investigation 2: 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 2.2 Using Tables, Graphs, and Equations KEY: y-intercept slope-intercept form 10