moving straight ahead - unit test review sheet straight ahead - unit test review sheet ... 1 dif: l2...

Name: ______________________ Class: _________________ Date: _________ ID: A

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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)

0 113 177 259 2910 31

3. Solve each equation for x. Show your work.a. 3x + 8 = 35 b. 12 + 5x = 7x + 3 c. 3(x + 1) = 12

4. 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.

Name: ______________________ ID: A

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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

Equationy = 1

3x + 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?

Name: ______________________ ID: A

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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 i i. D = 4.2t + 32 i i i. 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 = 29.7 – 0.2w .

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 = 20d. 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 – 4.5d. y = 2.6x e . y = 7x + 1

Name: ______________________ ID: A

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14. For each of the lines below, find the slope, and write an equation that represents the line.

Name: ______________________ ID: A

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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 + 2Line 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.

Name: ______________________ ID: A

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Multiple ChoiceIdentify 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 = 4x2 D. y = 2x

Use the following table to answer questipns 3-5.

X 1 2 3 4Y 4 7 10 13

____ 3. What is the slope of data set?

A. 4 B. 3 C. 1 D. 9

____ 4. What is the y-intercept of the data set?

A. 4 B. 3 C. 1 D. 13

____ 5. What is the equation to represent the data set?A. y = x + 3 C. y = 3x + 1B. y = 4x + 1 D. y = 3x +13

____ 6. Consider the equation y = 4x – 10. Find y if x = 3.A. 33 B. 12 C. 2 D. –3

____ 7. What is the equation of the line that contains the points (2, 13) and (6, 33)?

A. y = 15

x + 3 C. y = 15

x + 5

B. y = 5x + 5 D. y = 5x + 3

Name: ______________________ ID: A

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Find the slope of the line that passes through the pair of points.

____ 8. (1, 7), (10, 1)

A. 32

B. − 23

C. − 32

D. 23

____ 9. (–5.5, 6.1), (–2.5, 3.1)A. –1 B. 1 C. –1 D. 1

____ 10. A student finds the slope of the line between (14, 1) and (18, 17). She writes 1 − 1718 − 14

. 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 = −2A. 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

−2+ 2 = 12

A. –20 B. –22 C. –26 D. –28

____ 13. 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. 55 + 10p = 1,245; 119 puzzles C. 10p – 55 = 1,245; 23 puzzles

B. 65p = 1,245; 20 puzzles D. 1,245 = 10p + 55; 130 puzzles

Name: ______________________ ID: A

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____ 14. Graph the points A(5, –4 ), B(1, –2), and C(3, 3) on the same coordinate plane.A. C.

B. D.

Name: ______________________ ID: A

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Graph the linear equation.

____ 15. y = 3x − 4A. C.

B. D.

Name: ______________________ ID: A

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____ 16. y = − 15

x + 4

A. C.

B. D.

____ 17. Find the slope of the line.

A. − 12

B. 12

C. −2 D. 2

Name: ______________________ ID: A

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____ 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 = − 12

x + 7.

A. − 12

; 7 B. 12

; 7 C. − 12

; –7 D. 12

; –7

ID: A

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Moving Straight Ahead - Unit Test Review SheetAnswer 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 TestOBJ: Investigation 4: Exploring Slope NAT: CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4dSTA: 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 + 11.

PTS: 1 DIF: L2 REF: Moving Straight Ahead | Unit TestOBJ: Investigation 2: Exploring Linear Functions With Graphs and TablesNAT: 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.2dTOP: Problem 1.2

3. ANS: a. x = 9 b. x = 4.5c. x = 3

PTS: 1 DIF: L2 REF: Moving Straight Ahead | Unit TestOBJ: Investigation 3: Solving Equations NAT: CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4cSTA: 7NY 7.A.8 | 7NY 7.A.10 TOP: Problem 3.4 KEY: solving equations | linear equations

ID: A

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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 BankOBJ: Investigation 2: Exploring Linear Functions With Graphs and TablesNAT: 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 EquationsKEY: linear function | comparing functions

5. ANS: On the appropriate screen you need to enter the equations Y1 = 300 + 20X and Y2 = 50 + 35X, 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 BankOBJ: Investigation 3: Solving Equations NAT: CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4cSTA: 7NY 7.A.8 | 7NY 7.A.10 TOP: Problem 3.5 Finding the Point of IntersectionKEY: solving equations | point of intersection

ID: A

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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 − 17 + 17 = 43 + 17

4n = 60

4n4

= 604

n = 15

PTS: 1 DIF: L2 REF: Moving Straight Ahead | Question BankOBJ: Investigation 3: Solving Equations NAT: CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4cSTA: 7NY 7.A.8 | 7NY 7.A.10 TOP: Problem 3.3 Writing EquationsKEY: solving equations | writing equations

ID: A

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7. ANS:

Table

Graph

Equation y = –3x + 8 y = 4x – 3 y = 13

x + 1

a. The y-intercepts are 8, –3, and 1.

b. The slopes are –3, 4, and 13

.

PTS: 1 DIF: L2 REF: Moving Straight Ahead | Question BankOBJ: Investigation 4: Exploring Slope NAT: CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4dSTA: 7NY 7.A.7 | 7NY 7.A.8 TOP: Problem 4.2 Finding the Slope of a LineKEY: slope | finding the slope of a line

ID: A

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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) + 32.b. Answers will vary.

PTS: 1 DIF: L2 REF: Moving Straight Ahead | Additional Practice Investigation 3 OBJ: Investigation 3: Solving Equations NAT: CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4cSTA: 7NY 7.A.8 | 7NY 7.A.10 TOP: Problem 3.1 Solving Equations Using Tables and GraphsKEY: solving equations | tables and graphs

10. ANS: a. r = 6 b. x = 10c. z = 64 d. w = –187

PTS: 1 DIF: L2 REF: Moving Straight Ahead | Additional Practice Investigation 3 OBJ: Investigation 3: Solving Equations NAT: CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4cSTA: 7NY 7.A.8 | 7NY 7.A.10 TOP: Problem 3.4 Solving Linear EquationsKEY: solving equations | linear equations

ID: A

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11. ANS: a. 24 – 5x = 4; 4 b. 2x + 17 = 7; x = –5

c. 4x + 14 = 16; x = 12

d. 14

x – 11 = 11; x = 88


12. ANS: a. x = 13

b. 3x = 13 so x = 133

c. –2x = 13 so x = −132

d. The numerators of the solutions are all 13; the denominators are the coefficients of x


13. ANS: a. slope is 2; y-intercept is –10b. slope is 4; y-intercept is 3c. slope is 4; y-intercept is –4.5d. slope is 2.6; y-intercept is 0e . slope is 7; y-intercept is 1

PTS: 1 DIF: L2 REF: Moving Straight Ahead | Additional Practice Investigation 4 OBJ: Investigation 4: Exploring Slope NAT: CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4dSTA: 7NY 7.A.7 | 7NY 7.A.8 TOP: Problem 4.2 Finding the Slope of a LineKEY: slope | finding the slope of a line

ID: A

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14. ANS: a. slope is 1; y = x

b. slope is – 43

; y = – 43

x

c. slope is –3; y = –3x

PTS: 1 DIF: L2 REF: Moving Straight Ahead | Additional Practice Investigation 4 OBJ: Investigation 4: Exploring Slope NAT: CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4dSTA: 7NY 7.A.7 | 7NY 7.A.8 TOP: Problem 4.4 Writing Equations with Two VariablesKEY: 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, 2012

= 53

gallons in 1

minute.

c. G = − 53

t + 45

d. Substitute 10 for t in the equation. You get G = 28.33 gallons of water left in the aquarium.e . Substitute 0 for G in the equation. You get t = 27 minutes.


16. ANS: a. The slopes are the same; the y-intercepts are different

b. y = 2x + K, where K is any number strictly between 2 and 0; for example, y = 2x + 13

Ê

Ë

ÁÁÁÁÁÁ

ˆ

˜̃̃˜̃̃

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.


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