Algebra 1 Name: MIDTERM REVIEW L 1.1.3...

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UCS Common Mid-Term Exam Algebra 1 REVEIW

Algebra 1 Name: _______________________________ MIDTERM REVIEW Part 1 Hour: ______ Date: _______________

L 1.1.3

1. What are the properties that should be used to isolate the variable in the equation?

3x + 11 = 5

A additive identity and multiplicative identity

B additive inverse and multiplicative identity

C additive identity and multiplicative inverse

D additive inverse and multiplicative inverse

L 1.1.3

2. Which property would best be used to solve this problem mentally?

4 × 32 × 25

A distributive

B commutative

C associative

D closure

L 1.1.2 3. Why is the product of two even integers always an even number? Let the even integers

be represented by 2a and 2b.

A 2a 2b = 2(a + b), which is always even

B 2a 2b = 4(ab), which is even when (ab) is even but odd when (ab) is odd

C 2a 2b = 2(ab) = (4a)b, which is always even

D 2a 2b = 4(ab) = 2 (2ab), which is always even

L 1.1.2

4. Why is the multiplicative inverse of a negative integer also negative?

A The product of a number and its multiplicative inverse equals -1, so the number must

be negative.

B The multiplicative inverse of a number is always negative.

C The product of a number and its multiplicative inverse equals 1, so the number must

be negative.

D The sum of a number and its multiplicative inverse equals 0, so the number and its

multiplicative inverse must have the same sign.

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A 1.1.1 5. Evaluate for x = 3.

A –11 B 1 C –6 D 11

A 1.1.1 6. Evaluate the following expression when x = – 2, y = 4, and z = 1.

2

2

3x y

z

A –20

B –10

C –8

D 6

A 1.1.1

7. Seven times the sum of a number and five is 75. Which equation represents the previous sentence?

A 7x = 75

B x + 5 = 75

C 7x + 5 = 75

D 7(x + 5) = 75

A 1.1.1

8. Which of the following best describes the expression below?

4x 3

A I earned $3 more than four times what I earned last week.

B I earned $3 minus four times what I earned last week.

C I earned $3 less than four times what I earned last week.

D I earned $3 more than four times the difference between what I earned this week and last week.

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A1.2.4 9.

A1.2.4

10.

A –3 < x < 3

C –36 < x < 8

B –8 < x < 3

D –8 > x > 3

A 2.4.2

11. Write a function rule that gives the total cost c(p) of p pounds of sugar if each pound costs $.59.

A C

B

D

A 2.4.2

12. A snail travels at a rate of 2.13 feet per minute. a. Write a rule to describe the function. b. How far will the snail travel in 9 minutes?

A ; 19.17 ft C ; 19.17 ft

B ; 4.23 ft

D ; 11.13 ft

0 2 4 6 80–2–4–6–8 0 10 20 30 400–10–20–30–40

0 5 10 15 200–5–10–15–20 0 5 10 15 200–5–10–15–20

A –36 < x < 14

C –17 > x > 8

B –17 < x < 8

D –8 < x < 8

0 10 20 30 400–10–20–30–40 0 5 10 15 200–5–10–15–20

0 5 10 15 200–5–10–15–20 0 2 4 6 80–2–4–6–8

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A 2.4.3 13. Crystal earns $4.50 per hour mowing lawns.

a. Write a rule to describe how the amount of money m earned is a function of the number of hours h spent mowing lawns.

b. How much does Crystal earn if she works 2 hours and 15 minutes? Be careful!

A ; $10.13 C ; $24.00

B ; $0.50

D ; $9.68

A 2.4.3

14. What situation does this function model? 15075.7)( xxf

A Bill has $157.75

B Bill earns $157.75 per week

C Bill starts with $7.75 and earns $150 per week

D Bill starts with $150 and earns $7.75 per week A1.2.1

15. Miguel gets billed $29.95 per month by the cell phone company, which includes 400 minutes of talk time. If he uses more than 400 minutes, then he is charged $0.15 per minute. Miguel has only $35.00 to spend each month on his cell phone bill. Which of the following inequalities can be solved to show the maximum number of minutes over 400, m, he can use each month?

A 29.95 + 0.15m 35

B 29.95 + 0.15m 35

C 29.95m + 0.15 35

D 29.95m + 0.15 35

A1.2.1

16. Solve the following inequality. 4x 8 – 24

A x –4

B x –4

C x –8

D x –8

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A2.1.1 17. Which graph is NOT the graph of a function?

A C

B D A2.1.1

18. Which of the following sets of ordered pairs represents a function?

A {(1, 3), (2, 4), (0, 5), (1, 6), (0, 7)}

B {(5, 0), (5, 1), (5, 2), (5, 3), (5, 4)}

C {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5)}

D {(1, 2), (2, 1), (1, 3), (3, 1), (1, 4)}

A2.1.1

19. Which of the following sets of ordered pairs represents a function?

A {(2, -4), (-2, -4), (0, -4), (1, -4)}

B {(-3, 0), (-3, 1), (-3, 2)}

C {(2,2), (-2,9), (3,0), (-3,4), (2, 5)}

D {(1, 1), (1, 3), (3, -2), (6, 5), (1, 4)}

x

y

-4 4

4

-4

x

y

-4 4

4

-4

x

y

-4 4

4

-4

x

y

-4 4

4

-4

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A2.1.1 20. Which of the following sets could be the domain and range for this function?

{(1, 3), (2, 4), (0, 5), (1, 6), (0, 7)}

A Domain: {0,1, 2} Range: {3, 4, 5, 6, 7}

B Domain: {3, 4, 5, 6, 7} Range: {0, 1, 2}

C Domain: {0,1, 1, 2} Range: {0, 1, 2}

D Domain: all real numbers Range: all real numbers

A2.1.1

21. Which of the following sets could be the domain and range for this function?

{(-3, 0), (-3, 1), (-3, 2)}

A Domain: {-3} Range: {-3, 0, 1, 2}

B Domain: {-3} Range: {0, 1, 2}

C Domain: {0, 1, 2} Range: {-3}

D Domain: {-3, 0, 1, 2} Range: {-3}

A2.1.7

22. A dolphin dove underwater following the parabolic path f(t)= t2 – 10t, where

d represents its depth in the water in feet and t is the time since its dive in seconds. What is the value of f(2)?

A -10 feet

B -16 feet

C -25 feet

D -100 feet

A2.1.7

23. An object is following the path modeled by the equation y -2x2 5x 8. What does the y-intercept of the graph represent? What does the maximum point represent?

A the point where the object hits the ground; the highest point the object reaches

B the point where the object hits the ground; the point from which the object is dropped

C the point from which the object is thrown; the highest point the object reaches

D the point from which the object is thrown; the point from which the object is dropped

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A2.1.2 24. In February, you have a balance of $270 in your bank account. Each month you

deposit $45. Let January = 1, February = 2, and so on. Write an equation for this situation. Use the equation to find the balance in June.

A y – 270 = 45(x – 2) ; $450 C y = 45(x – 4); $180

B y = 45(x – 4); $270 D y – 270 = 45x; $45 A2.1.2

25. Sarah pays $210 in advance on her account at the athletic club. Each time she uses the club, $10 is deducted from the account. The situation can be modeled by the equation b = 210 – 10x, where x is the number of visits and b is the total account balance.

a. Graph the equation. b. Find the account balance after 8 visits.

A

$140

C

$290

B

$130

D

$110

Athletic Club Account

1 2 3 4 5 6 7 8 9 x

40

80

120

160

200

240

280

b Athletic Club Account

1 2 3 4 5 6 7 8 9 x

40

80

120

160

200

240

280

320

360

400b

Athletic Club Account

1 2 3 4 5 6 7 8 9 x

40

80

120

160

200

240

280

b Athletic Club Account

1 2 3 4 5 6 7 8 9 x

40

80

120

160

200

240

280

b

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A1.2.1 26. An equilateral triangle has three sides of equal length. What is the equation for the

perimeter of an equilateral triangle if P = perimeter and s = length of a side?

A. s = 3P B. P = 3s C. P = 3 + s D. P = 3(s + s + s)

A1.2.2

27. The length of a rectangle is 3 centimeters more than 3 times the width. If the perimeter of the rectangle is 46 centimeters, find the dimensions of the rectangle.

A length = 5 cm; width = 18 cm C length = 13 cm; width = 8 cm

B length = 13 cm; width = 5 cm D length = 18 cm; width = 5 cm A2.3.2

28. The rate of change is constant in the table. Find the rate of change. Explain what the rate of change means for the situation.

Time (days) Cost ($)

3 75

4 100

5 125

6 150

A dollars per day; the cost is $25 for each day.

B dollars per day; the cost is $25 for each day.

C dollars per day; the cost is $75 for each day.

D dollars per day; the costs $1 for 150 days

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Algebra 1 Name: _______________________________ MIDTERM REVIEW Part 2 Hour: ______ Date: _______________ A2.3

29. The rate of change is constant in the table. Find the rate of change. Explain what the rate of the change means for the situation.

Time (hours) Distance (miles)

4 260

6 390

8 520

10 650

A 10; Your car travels for 10 hours.

B 260; Your car travels 260 miles.

C

; Your car travels 65 miles every 1 hour.

D ; Your car travels 65 miles every 1 hour.

A2.1.3

30. Which of the following equations represents the graph below?

A y 2

3x + 2

B y -2

3x + 2

C y 2x + 2

3

D y -2x + 2

3

y

x 0 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6

1

-5

-4

-3 -2

-1

2

3 4

5 6

-6

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A2.1.3

31. Match the equation with its graph. –7x + 7y = –49

A

C

B

D

A.3.1.1

32. Write an equation in point-slope form for the line through the given point with the given slope.

(4, –6); m =

A C

B D

2 4 6 8 10–2–4–6–8–10 x

2

4

6

8

10

–2

–4

–6

–8

–10

y

2 4 6 8 10–2–4–6–8–10 x

2

4

6

8

10

–2

–4

–6

–8

–10

y

2 4 6 8 10–2–4–6–8–10 x

2

4

6

8

10

–2

–4

–6

–8

–10

y

2 4 6 8 10–2–4–6–8–10 x

2

4

6

8

10

–2

–4

–6

–8

–10

y

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1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

A.3.1.1 33. A line passes through (1, –5) and (–3, 7).

a. Write an equation for the line in point-slope form. b. Rewrite the equation in slope-intercept form.

A y – 5 = 3(x + 1); y = 3x + 8 C

B ;

D y + 5 = –3(x – 1); y = –3x – 2

A3.1.2

34. Which of the following is the equation of the graph below? A3.1.2

35. Which of the following is the equation of the graph below.

A x = -2

B y = -2

C x = 2

D y = 2

A x = -4

B y = -4

C x = 4

D y = 4

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A3.1.3 36. Find the slope and y-intercept of the line. 14x + 4y = 24

A ; C ;

B ; D ;

A3.1.4 37. Which of the following represents a line that is parallel to the line

y = 4x 2?

A y -4x

B y -1

4x

C y 1

4x

D y 4x

A3.1.4

38. Which of the following lines is perpendicular to y -1

3x – 1 and passes through the

point (2, 5)?

A y 3x

B y 3x + 5

C y 3x – 1

D y -3x – 5

A3.1.4

39. Which statement is true about these equations?

y = x – 5 y = -x + 5

A The equations represent parallel lines.

B The equations represent perpendicular lines.

C The equations represent intersecting lines that are not perpendicular.

D The equations represent the same line.

2

76

7

2

1

6

7

26

7

26

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A1.2.3 40. Solve the system of equations using substitution.

3x + 2y = 7

y = –3x + 11

A (6, –3) B (6, –7) C

D (5, –4)

A1.2.3

41. Solve the system using elimination.

x + 2y = –6 3x + 8y = –20

A (–1, –4) B (–4, 4) C (–4, –1) D (3, 1)

A2.2.2

42. How can the graph of y = x be translated so that its equation

becomes y = x 1 + 3?

A It can be shifted right 3 units and up 1 unit.

B It can be shifted left 3 units and down 1 unit.

C It can be shifted right 1 unit and up 3 units.

D It can be shifted left 1 unit and down 3 units. A2.2.2

43. How does the graph of the function ( ) | | compare with the graph of

( ) | |?

A It is vertically stretched by a factor of 3 and shifted down 2 units.

B It is vertically stretched by a factor of 3 and shifted right 2 units.

C It is horizontally stretched by a factor of 3 and shifted down 2 units.

D It is horizontally stretched by a factor of 3 and shifted right 2 units.

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A3.3.2 44. Examine the graph below. What do you know about the standard form of the

equation of this parabola? ( )

A A is positive and C is negative.

B A is negative and C is positive.

C Both A and C must be positive.

D Both A and C must be negative.

A3.3.2

45. The graph shown below is y x2. How would the graph y -4x2 5 differ from the

given graph?

A It is vertically stretched by a factor of 4, opens down, and moves up 5 units.

B It is vertically stretched by a factor of 4, opens up, and moves down 5 units.

C It is horizontally stretched by a factor of 4, opens down, and moves up 5 units.

D It is horizontally stretched by a factor of 4, opens up, and moves down 5 units.

0

5

10

15

20

25

-5 -4 -3 -2 -1 0 1 2 3 4 5

x

y

1 2 3 4 9 8 7 6 5 1 2 3 4 5 6 7 8 9

-1 -2

-3

-4 -5 -6 -7

-8 -9

-1 -2

-3

-4 -5 -6 -7

-8 -9 0

y

x

Page | 15


A1.2.2

46. What are the zeros of the function: y = x 2 – x – 12?

A x = 1 or x = -12

B x = -1 or x = 12

C x = -4 or x = 3

D x = 4 or x = -3

A1.2.2

47. The graph of a quadratic equation intersects the x-axis in exactly one point. Which of the following statements is/are true?

A The equation has one zero.

B The discriminant is zero.

C The equation is of the form y = a(x – b) 2 .

D A, B, and C are true.

A3.3.4

48. If the vertex of the graph of a quadratic function is located on the x-axis, how many distinct real solutions does the equation have?

A 0

B 1

C 2

D 3

A3.3.4

49. The graph of the equation y = x2 + 4 opens up with a vertex at (0, 4). How many real solutions does the equation have?

A no real solutions

B 1 real solution

C 2 real solutions

D number of real solutions cannot be determined A1.1.3

50. What is the factored form of 16x4 – 9y2

A (4x – 3y)2

B (4x – 3y)(4x + 3y)

C (4x2 – 3y)2

D (4x2 – 3y)(4x2 + 3y)

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A1.1.3 51. Factor the following expression.

12x2 60x + 75

A 3(4x – 25)(x – 1)

B 3(2x – 5)(2x + 5)

C 3(4x – 5)(x – 5)

D 3(2x – 5)2

A3.3.5

52. Find the zeros of the function. y = (3x – 1) (x + 7)

A x = 3

1 , x = -7

B x = 3

1½ , x = 7

C x = 3

1 , x = -7

D x = 3

1 , x = 7

A2.1.7

53. What is the maximum value of the function f(x) = –2x2 + 12x + 14

A -4

B 32

C –40

D 68

A3.3.2

54. What is the line of symmetry in the graphed quadratic function?

A x = -1

B x = -3

C y = -1

D y = -3

1 2 3 4 9 8 7 6 5

1 2 3 4 5 6 7 8 9

-1 -2

-3

-4 -5 -6 -7

-8 -9

-1

-2

-3

-4 -5 -6 -7

-8 -9 0

y

x

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A3.3.2 55. Find the equation of the axis of symmetry and the coordinates of the vertex of the

graph of the function.

A ; vertex: C ; vertex:

B ; vertex: D ; vertex:

A1.1.3

56. Factor the following expression. 12x2 60x + 75

A 3(4x – 25)(x – 1)

B 3(2x – 5)(2x + 5)

C 3(4x – 5)(x – 5)

D 3(2x – 5)2

A1.1.3

57. Factor the following expression 64x4 – 36y2 =

A (8x – 6y)2

B (8x – 6y)(8x + 6y)

C 4(4x2 – 3y)2

D 4(4x2 – 3y)(4x2 + 3y)

A3.3.3

58. Which of the following represents the vertex form of the equation: y =x2 – 4x – 6?

A y = (x + 2)2 + 2

B y = (x – 2)2 + 2

C y = (x + 2)2 – 10

D y = (x – 2)2 – 10

A3.3.3

59. Which of the following represents the vertex form of the equation: y = 2x2 + 4x + 8?

A y = 2(x + 2)2

B y = 2(x + 2)2 + 4

C y = 2(x + 1)2 + 6

D y = 2(x + 1)2 + 7

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2010 – 2011 UCS ALGEBRA 1 HIGH SCHOOL SEMESTER 1 EXAM REVIEW

A1.2.3 60. Solve the following equation using the quadratic formula. x2 5x 3 0

A x

-5 13

2

B x

5 13

2

C x

-5 37

2

D x

5 37

2

A1.2.3

61. Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.

A 18, 28 B –9, –14 C 9, 14 D –18, 28

L2.1.4 62. Simplify the following: i -320

A 1

B -1

C -i

D I

L2.1.4

63. Simplify the expression. √

A –12i

B 12i

C 144i

D 12

A1.2.8 64. The formula for the perimeter of a rectangle is shown below.

Solve the formula for the variable l.

P = 2l + 2w

A l = P w

B l = P 2w 2

C l = P

w2

D l = P w

2

Page | 19


A1.2.8 65. The formula for a circle centered at the origin is shown below. Solve the equation for y.

x2 + y2 = r2

A y = r x

B y = x r

C y = r x2 2

D y = x r2 2

A 2.1.6

66. What are the zeros of the function?

A )0,11()0,9( and C )0,11()0,9( and

B )0,11()0,9( and D )0,11()0,9( and

A2.1.6

67. What are the zeros of the function? )15)(3(5 xxy

A )0,15()0,3( and C )0,15()0,3()0,5( andand

B )0,15()0,3()0,5( andand D )0,15()0,3( and

A2.1.6

68. What are the zeros of the function? 1282 xxy

A )0,2()0,6( and C )0,2()0,6( and

B )0,2()0,6( and D )0,2()0,6( and

A2.1.6

69. What are the zeros of the function? 2082 xxy

A )0,10()0,2( and C )0,10()0,2( and

B )0,10()0,2( and D )0,10()0,2( and

Page | 20


A2.4.1 70. In February, you have a balance of $270 in your bank account. Each month you deposit $45. Which

type of function would best model this situation?

A Linear C Quadratic

B Exponential D Absolute Value

A2.4.1 71. A rocket is launched from atop a 101-foot cliff with an initial velocity of 116 ft/s.

Which function would best model this flight pattern of the rocket?

A Linear C Exponential

B Quadratic D Absolute Value

A3.3.1 72. Which of the following represents the graph of a quadratic equation whose maximum

is found at ( )?

A ( )

B ( )

C ( )

D ( )

A3.3.1 73. Which of the following represents the graph of a quadratic equation whose minimum

is found at ( )?

A ( )

B ( )

C ( )

D ( )

Page | 21


Algebra 1 Name: _______________________________ MIDTERM REVIEW Part 3 Hour: ______ Date: _______________

74. Which of the following is the equation of a parabola with a vertex of (4, 0) and a y-intercept

of (0, 8)?

A y = 1

2(x – 4)2

B y = 1

2(x + 4)2

C y = 2(x – 4)2

D y = 2(x + 4)2

75. Which is always the correct conclusion about the quantities in the function y = x – 12?

A The variable x is always 12 more than y.

B When the value of x is positive, the value of y is also positive.

C The variable of y is always 12 less than x.

D The value of x decreases, the value of y increases.

L1.2.2 76. What is the solution to |x – 5| 7

A –35 x 35

B –12 x 12

C –12 x 2

D –2 x 12

L1.2.2 77. The length of a bolt used in a car door is supposed to be 3 cm. The actual length can vary by

at most 0.2 cm. Write an absolute value inequality for the range of acceptable lengths.

A | |

B | |

C | |

D | |

78. Solve the equation. 2(y – 5) = 2

A 6 B 5 C –4 D 4

Page | 22


79. Solve the equation.

A 28 B C D 3

80. Solve the equation. 2x – 8 = 4x + 4

A –9 B –3 C –6 D 2

81. Solve the equation. 9d + d + 4d + 2 = 3d

A 8 B

C

D

82. Solve the inequality. –5x – 7 < 28

A x > –7 B x < –7 C

D

83. Solve the inequality.

A B C D

A.1.2.3 84. Solve the system of equations using substitution.

2x + 5y = 25

x + 20y = 65

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

2

11

2

3

2

17

Page | 23


A.1.2.3 85. Solve the system using elimination. x + 3y = 8

4x + 6y = 8

A (4, 1) B (–4, 2) C (4, –4) D (–4, 4)

A.1.2.3 86. Solve the system using elimination. 2x + 5y = 25

x + 20y = 65

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

87. Factor the expression. d 2 + 10d + 9

A (d + 9)(d – 1) C (d – 9)(d – 1)

B (d – 9)(d + 1) D (d + 9)(d + 1)

88. Factor the expression.

A C

B D

89. Factor the expression. 3x2 + 7x – 6

A (3x – 2)(x – 3) C (x + 3)(3x + 2)

B (3x – 2)(x + 3) D (3x + 2)(x – 3)

90. Factor the expression. 21m2 – 29m – 10

A (7m – 2)(3m – 5) C (7m + 2)(3m – 5)

B (7m + 2)(3m + 5) D (7m – 2)(3m + 5)

Page | 24


1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

1

4

4

4

91. Simplify the product. 7a3(5a6 – 2b3)

A 12a 9 – 9a 3b 6 C 35a 9 – 14a 3b 3

B 35a 9 – 14ab 6 D 12a 18 – 9a 3b 6

92. Find the slope of the line that passes through the pair of points: (5, 4), (8, 0)

A

B

C

D

93. Find the slope of the line.

A

B

C

D

94. Write an equation of a line with the given slope and y- intercept. m = –2, b = –10

A y = –2x + 10 C y = 2x – 10

B y = –2x – 10 D y = –10x – 2

95. Write an equation of a line with the given slope and y-intercept. m = , b =

A y = x –

C y = x +

B y = x –

D y = x +

3

4

3

4

4

3

4

3

1

4

1

4

3

4

43

4

3

4

1

4

1

4

3

4

1

4

3

4

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96. Find the x- and y-intercept of the line. 4x + 3y = –12

A x-intercept is -3; y-intercept is -4. C x-intercept is -4; y-intercept is -3.

B x-intercept is 4; y-intercept is –3. D x-intercept is 0; y-intercept is 4.

97. Graph .

A

C

B

D

98. Write an equation in slope-intercept form for the line through the given point with

the given slope. (–10, 2); m =

A 103 xy C 283 xy

B 283 xy D 283 xy

2 4 6 8–2–4–6–8 x

2

4

6

8

–2

–4

–6

–8

y

2 4 6 8–2–4–6–8 x

2

4

6

8

–2

–4

–6

–8

y

2 4 6 8–2–4–6–8 x

2

4

6

8

–2

–4

–6

–8

y

2 4 6 8–2–4–6–8 x

2

4

6

8

–2

–4

–6

–8

y

3

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1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

99. Write the equation for the line. State whether the slope is 0 or undefined.

100. Write the equation for the line. State whether the slope is 0 or undefined.

A 2x slope is undefined

B 2x slope is 0

C 2y slope is undefined

D 2y slope is 0

A 2x slope is undefined

B 2x slope is 0

C 2y slope is undefined

D 2y slope is 0

Algebra 1 Name: MIDTERM REVIEW L 1.1.3...

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