module 1-a1.1.2- linear equations 2.pdfmodule 1-a1.1.2- linear equations 14. the accompanying graph...

Module 1-A1.1.2- Linear Equations

Name: Date:

1. Solve for x: 4(x − 2) − 3 = 9

2. Solve for x: 23x − 1 = 5

3. The solution of the equation 3(x + 3) = 12 is

A. 1 B. 2 C. 3 D. 4

4. Solve for x: 6(x + 1) = 4x

5. Which value of p is the solution of 5p − 1 = 2p + 20?

A. 197 B. 19

3 C. 3 D. 7

6. Solve for x: 5x − 21 = 8x − 30

7. Solve for x: 7(x − 2) = 5(x + 4)

8. Solve for x: 6(x − 2) − 4x = 16

9. Solve for t: 3t + 5(6 − t) = 4

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10. What is the value of x in the equation 4(2x + 1) = 27 + 3(2x − 5)?

A. 21 B. 9 C. 7 12 D. 4

11. What is the value of x in the equation 13x − 2(x + 4) = 8x + 1?

A. 1 B. 2 C. 3 D. 4

12. Solve algebraically for x:3

4=−(x + 11)

4x+

1

2x

13. What is the solution for the equation x + 1 = x + 2?

A. −1 B. 12 C. all real numbers D. There is no solution.

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14. The accompanying graph represents the yearly cost of playing 0 to 5 games of golf at the Shadybrook Golf Course.What is the total cost of joining the club and playing 10 games during the year?

15. If x and y are defined as indicated by the accompanying table, which equation correctly represents the relationshipbetween x and y?

x y

2 1

3 3

5 7

7 11

A. y = x + 2 B. y = 2x + 2 C. y = 2x + 3 D. y = 2x − 3

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16. John left his home and walked 3 blocks to his school, as shown in the accompanying graph.

What is one possible interpretation of the section of the graph from point B to point C?

A. John arrived at school and stayed throughout the day.

B. John waited before crossing a busy street.

C. John returned home to get his mathematics homework.

D. John reached the top of a hill and began walking on level ground.

17. Which equation expresses the relationship between x and y, as shown in the accompanying table?

x 0 1 2 3 4

y 2 5 8 11 14

A. y = x + 3 B. y = 2x + 3 C. y = 3x + 2 D. y = x + 2

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18. Granola bars cost $0.55 each. Which table represents this relationship?

A. B.

C. D.

19. Antwaan leaves a cup of hot chocolate on the counter in his kitchen. Which graph is the best representation of thechange in temperature of his hot chocolate over time?

A. B.

C. D.

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20. Which graph represents a function?

A. B. C. D.

21. Which diagram shows a relation that is not a function?

A. B. C. D.

22. Which graph does not represent a function?

A. B.

C. D.

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23. Which graph does not represent a function of x?

A. B.

C. D.

24. Which graph is not a function?

A. B. C. D.

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25. Which graph represents a linear function?

A. B.

C. D.

26. Given the relation R = {(−2, 3), (a, 4), (1, 9), (0, 7)}. Which placement for a makes this relation a function

A. 1 B. −2 C. 0 D. 4

27. Which set of ordered pairs is not a function?

A. {(3, 1), (2, 1), (1, 2), (3, 2)} B. {(4, 1), (5, 1), (6, 1), (7, 1)}

C. {(1, 2), (3, 4), (4, 5), (5, 6)} D. {(0, 0), (1, 1), (2, 2), (3, 3)}

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28. Which relation is not a function?

A. {(1, 5), (2, 6), (3, 6), (4, 7)} B. {(4, 7), (2, 1), (−3, 6), (3, 4)}

C. {(−1, 6), (1, 3), (2, 5), (1, 7)} D. {(−1, 2), (0, 5), (5, 0), (2,−1)}

29. What is an equation of the line whose graph is shown?

A. y = −x B. y = 2x C. y = x D. y = 2

30. Which is the graph of the equation y = 2?

A. B. C. D.

31. In the accompanying diagram, which is an equation of line ` ?

A. y = 3 B. x = 3 C. x + y = 3 D. x − y = 3

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32. Which graph represents the equation x = −3?

A. B. C. D.

33. What is the equation of the line in the accompanying graph?

A. 2y = x − 2 B. y = 12x + 1 C. y = −2x − 2 D. y = 2x − 2

34. Which graph represents the graph of the equation x = 2?

A. B.

C. D.

page 10


35. Which equation is equivalent to x + 2y = 6?

A. y = −x + 6 B. y = − 12x − 6 C. y = −x + 3 D. y = − 1

2x + 3

36. A line is represented by the equation y = 3x − 7. Which statement about the line is true?

A. The slope of the line is 13 .

B. The y-intercept is −7.

C. Point (1, 4) lies on the line.

D. This line is parallel to the line whose equation is y = 2x − 7.

37. The graph of which equation does not pass through the origin?

A. y = x B. y = −x C. y = 0 D. y = 1

38. Which is an equation of the line that passes through the points (1, 3) and (−1, 1)?

A. x = 1 B. y = 2x + 1 C. y = x + 2 D. y = 3

39. Which statement is true about the lines formed by the graphs of the equations y = x − 3 and x = y − 3?

A. They are identical. B. They intersect but are not perpendicular.

C. They are parallel. D. They are perpendicular.

page 11


40. The line 3x − 2y = 12 has

A. a slope of 32 and a y-intercept of −6 B. a slope of − 3

2 and a y-intercept of 6

C. a slope of 3 and a y-intercept of −2 D. a slope of −3 and a y-intercept of −6

41. Which statement describes the graph of x = 4?

A. It passes through the point (0, 4). B. It has a slope of 4.

C. It is parallel to the y-axis. D. It is parallel to the x-axis.

42. Which equation represents a line whose slope is 12 and whose y-intercept is 3?

A. y = 12x − 3 B. y = − 1

2x + 3 C. y = 3x + 12 D. y = 1

2x + 3

43. The graph of which equation passes through points (0, 6) and (4,−1) ?

A. y = 74x + 6 B. y = 4

7x + 6 C. y = − 74x + 6 D. y = − 4

7x + 6

44. Which is an equation of the line that passes through the point (5,−2) and has a slope of −3?

A. y = −3x − 13 B. y = 3x − 13 C. y = −3x + 13 D. y = 3x + 13

45. What is the slope of a line perpendicular to the graph of the equation 5x − 3y = 2?

A. − 35 B. − 1

5 C. 53 D. 5

page 12


46. Lines ` and m are perpendicular. If the slope of line m is − 43 , what is the slope of line ` ?

47. The slope of a line perpendicular to the line whose equation is y = 3x − 4 is

A. 13 B. −3 C. −1 D. − 1

3

48. If line ` is perpendicular to line m and the slope of line ` is undefined, what is the slope of line m ?

A. 1 B. 12 C. 0 D. −1

49. If the slope of←→JK is 3

4 and←→JK ⊥

←→PQ, what is the slope of

←→PQ ?

50. If two lines are parallel and the slope of one of the lines is m, what is the product of their slopes?

A. 1 B. 2m C. m2 D. 0

51. Which statement describes the lines whose equations are y = 13x + 12 and 6y = 2x + 6?

A. They are segments. B. They are perpendicular to each other.

C. They intersect each other. D. They are parallel to each other.

52. The graph of which equation would not be parallel to the graph of the equation y = 3x + 3?

A. y = 3x B. 2y = 6x + 2 C. y − 3x = 4 D. y = 2x + 3

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53. Which equation represents a line that is parallel to the line whose equation is y = 3x − 1?

A. y = − 13x + 1 B. y = 1

3x − 1 C. y = −3x − 1 D. y = 3x + 1

54. Which equation represents a line that is parallel to the line y = 3 − 2x?

A. 4x + 2y = 5 B. 2x + 4y = 1 C. y = 3 − 4x D. y = 4x − 2

55. Write an equation of the line that passes through the point (6,−5) and is parallel to the line whose equation is2x − 3y = 11.

56. Which equation represents a line parallel to the graph of 2x − 4y = 16?

A. y = 12x − 5 B. y = − 1

2x + 4 C. y = −2x + 6 D. y = 2x + 8

57. Which is an equation of a line perpendicular to the line whose equation is y = − 12x + 5?

A. y = 2x − 1 B. y = −2x − 1 C. y = 12x − 1 D. y = − 1

2x − 1

58. Which equation represents a line that is perpendicular to the line whose equation is y = 23x + 4?

A. y = − 23x − 4 B. y = − 3

2x + 4 C. y = − 23x + 4 D. y = 3

2x + 4

59. Find an equation of the line passing through the point (6, 5) and perpendicular to the line whose equation is2y + 3x = 6.

page 14


60. What is an equation of the line that contains the point (3,−1) and is perpendicular to the line whose equation isy = −3x + 2?

A. y = −3x + 8 B. y = −3x C. y = 13x D. y = 1

3x − 2

61. Solve the following systems of equations for x:

2x + 3y = 54x − 3y = 1

62. Solve the following system of equations graphically and check:

3x + y = 3y = 2x − 7

63. What is the solution for the following system of equations?

2x + y = 7x − 2y = 6

A. (3, 1) B. (1, 3) C. (−1, 4) D. (4,−1)

64. Solve the following system of equations for x:

3x + 2y = 212y = 18

65. Solve the following system of equations algebraically and check:

3x − 2y = 222x + 5y = 2

page 15


66. Which ordered pair is the solution to this system of equations?

y = x + 4x + y = 2

A. (1, 5) B. (0, 2) C. (−1, 3) D. (−4, 0)

67. Solve the following system of equations algebraically or graphically and check:

3y = 2x − 6x + y = 8

68. What is the solution for x in the following system of equations?

−y = 2x − 3y = −x + 1

A. 23 B. 2 C. 4

3 D. 4

69. Solve the following system of equations algebraically and check.

0.7x + 0.4y = 16x + y = 10

70. What is a solution for the system of equations x − y = 2 and y = 2x − 4?

A. (0, 2) B. (2, 0) C. (3, 2) D. (4, 2)

71. When solved graphically, which system of equations will have exactly one point of intersection?

A. y = −x − 20y = x + 17

B. y = 0.5x + 30y = 0.5x − 30

C. y = 35x + 12

y = 0.6x − 19

D. y = −x + 15y = −x + 25

page 16


72. The two lines represented by the equations below are graphed on a coordinate plane.

x + 6y = 123(x − 2) = −y − 4

Which statement best describes the two lines?

A. The lines are parallel. B. The lines are the same line.

C. The lines are perpendicular. D. The lines intersect at an angle other than 90◦.

73. Fame and Fortune

The agent for a group of musicians has presented the following two contracts for their first CD recording:

Contract A: The recording company will pay them $1.50 per CD sold, but thegroup must pay $50,000 production costs from their profits.

Contract B: The recording company will pay them $0.50 per CD sold, with nocharge for production costs.

What is the difference in profit (if any) between options A and B when 50,000 CDs have been sold?

74. Ticket Prices

The chart below shows the ticket prices for events at the Community Stadium and Arena.

SPORT CHILD ADULT

Hockey $4.50 $7.00

Basketball $5.00 $9.00

Football $6.25 $11.50

A scout troop spent $80.75 for children and adult tickets to a football game. How many adults and how manychildren must have been in the group?

page 17


75. College Savings

Juan’s family is saving money for Juan to go to college. They currently have $2,500 in the bank and save $150each month. Alex’s family is also saving for college. They currently have $900 in the bank and save $250 permonth.

When will both families have the same amount of savings? Show how you arrived at your solution.

76. For an original graphic design, Lee charges a fixed fee of $50 plus $25 for each hour that he works. His maincompetitor charges a fixed fee of $40 plus $30 for each hour that he works on a design. Lee’s competitor advertisesthat his rates are cheaper. Is Lee’s competitor correct? Explain your reasoning.

77. Julio interviews for two jobs. Both jobs offer him a starting salary of $20,000, but the first job includes a $1,030raise every year, while the second job includes a 5% raise every year.

After how many years will the salary for the second job exceed the salary of the first job?

78. Sally and her friend Lucie started saving money for their vacation on the same day. Sally started with $150 andplans to add $5 to the total every week. Lucie started with $200 and plans to add $3 to the total every week.

After how many weeks will Sally’s savings be the same as Lucie’s savings?

page 18


79. A flower shop sells the two flower arrangements shown below.

Each rose has the same price, and each daisy has the same price. What is the price of one rose?

A. $3 B. $6 C. $9 D. $12

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80. Use the information in the box below to answer the question.

Misha and his sister are using 5-foot and 8-foot landscaping timbers to enclose a vegetable garden. They bought40 timbers. The total cost for the timbers was $288. Which pair of equations could be used to find the number oftimbers of each size that they bought?

A. 6x + 9y = 40 and x + y = 288 B. x + y = 40 and 5x + 8y = 288

C. 5x + 8y = 40 and 6x + 9y = 288 D. x + y = 40 and 6x + 9y = 288

page 20

Acces format version 4.4.170c_ 1997–2011 EducAide Software

Licensed for use by Tammie Wilkes

Module 1-A1.1.2- Linear Equations 04/08/2013

1.Answer: 5

2.Answer: 9

3.Answer: A

4.Answer: −3

5.Answer: D

6.Answer: 3

7.Answer: 17

8.Answer: 14

9.Answer: 13

10.Answer: D

11.Answer: C

12.Answer: − 4

9

13.Answer: D

14.Answer: $390

15.Answer: D

16.Answer: B

17.Answer: C

18.Answer: B

19.Answer: A

20.Answer: D

21.Answer: A

22.Answer: D

23.Answer: A

24.Answer: A

25.Answer: A

26.Answer: D

27.Answer: A

28.Answer: C

29.Answer: C

30.Answer: B

31.Answer: B

32.Answer: B

33.Answer: D

34.Answer: A

35.Answer: D

36.Answer: B

37.Answer: D

38.Answer: C

39.Answer: C

Teacher’s Key Page 2

40.Answer: A

41.Answer: C

42.Answer: D

43.Answer: C

44.Answer: C

45.Answer: A

46.Answer: 3

4

47.Answer: D

48.Answer: C

49.Answer: − 4

3

50.Answer: C

51.Answer: D

52.Answer: D

53.Answer: D

54.Answer: A

55.Answer: y + 5 = 2

3 (x − 6)

56.Answer: A

57.Answer: A

58.Answer: B

59.Answer: y − 5 = 2

3 (x − 6)

60.Answer: D

61.Answer: 1

62.Answer: [graph]

63.Answer: D

64.Answer: 1

65.Answer: x = 6 and y = 2

66.Answer: C

67.Answer: (6, 2)

68.Answer: B

69.Answer: (40,−30)

70.Answer: B

71.Answer: A

72.Answer: D

73.

74.

75.

76.

77.Answer: 3

78.

79.Answer: B

80.Answer: D

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