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8.F.4 [560511]StudentClassDate

1. The table below shows the dolphin population in an area in 1990 and 1995.

Year Number of

Dolphins1990 1471995 196

Based on a linear model, what will be the approximatedolphin population in 2015?

A. 297

B. 392

C. 441

D. 490

2. The graph shows the relationship between distance and time for a train traveling on a 104-mile section of train tracks.

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The equation d=1.05t represents the distance, d miles, that a car can travel in t minutes.

Part A What is the difference in the times, to the nearest whole minute, it would take the train and the car to travel 45 miles at their average speeds?

Part B What is the average speed, to the nearest whole miles per hour, for the train?

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Part C Which is faster, the train or the car?

Part D Mr. Bretz asked his students to describe the slope in the graph.

Thomas says the slope represents the distance the train travels. Riley says the slope represents the distance the train travels in one

minute. Carrie says the slope represents the amount of time the train travels.

Which student is correct?

3. The points (–3, –5), (0, 4), and (3, 13) lie on the same line. Which equation describes the function for that line?

A. y = 2x + 1

B. y = 3x + 4

C. y = x + 4

D. y = x + –2

4. What is the equation of a line that passes through the point (–6, 5) and is parallel to the x-axis?

A. x = –6

B. y = 5

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C. y = x – 6

D. x = y – 5

5. Which is an equation of the line that passes through the points (–4,

–2) and (4, 2)?

A.

B.

C.

D.

6. The table below shows the cost of a large scoop of ice cream with toppings at an ice cream shop.

Number of Toppings

Cost

3 $4.064 $4.656 $5.83

What is the cost of a large scoop of ice cream with no toppings?

A. $3.47

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B. $2.29

C. $1.35

D. $0.59

7. In January, David began putting the same amount of money each month into his savings account.

In February, he had $85.00 in his account, not including interest.

By June, he had $135.00 in his account, not including interest.

How much money was in the savings account before David began saving each month?

A. $12.50

B. $50.00

C. $60.00

D. $72.50

8. A car rental company charges a daily fee, plus an additional fee for each mile driven. Susan rented a car for one day, drove 100 miles, and was charged $48.00. Bob rented a car for one day, drove 224 miles, and was charged $72.80. How much does the company charge for a one-day rental and 172 miles driven?

A. $56.60

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B. $60.40

C. $62.40

D. $68.00

9. Which is an equation of a line passing through the point (–2, 2) with a y-intercept of 1?

A.

B.

C.

10. Exploration of FunctionsEric’s car can travel 25 miles on one gallon of gasoline. A gallon of gasoline costs $3.30.TASK:Part AConstruct function G to represent the amount of money Eric spends on gasoline based on the distance he drives, d.Part BWhat is the function’s rate of change? Interpret the rate of change for G in this context.Part CRepresent G on a graph.

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Part DEric wants to keep track of how far he can travel for every $100 he spends on gasoline. He constructs function D to represent the distance he travels based on the amount he spends on gasoline, g.The initial value of D is 0. Should that value be interpreted differently from the initial value of G? Explain why or why not.Part EInterpret what the rate of change of D would signify in this context.

11. A car rental company rents only one type of car. The table shows the cost to rent a car from the company.

The rental cost includes a one-time base fee plus a constant rate for each day that a customer rents a car. What is the company’s base fee?

A. $13

B. $39

C. $46

D. $59

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12. Which equation models the linear relationship in the table below?

A.

B.

C.

D.

13. Which is the equation of the line that passes through the points (0, –2) and (–1, –7)?

A. y = –9x – 2

B. y = –5x – 2

C. y = 5x – 2

D. y = 9x – 2

14. Which function, when graphed, will be a line that passes through

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the points (–3, –2) and (1, 6)?

A. y = 0.5x + 6

B. y = x + 1

C. y = x + 5

D. y = 2x + 4

15. Which is an equation of the line with a slope of 1.5 that passes through the point (–8, –9)?

A. y = 5.5x + 1.5

B. y = 3x + 1.5

C. y = 1.5x + 5.5

D. y = 1.5x + 3

16. A printing company makes business cards.

The company charges a one-time design fee, plus a charge for each business card printed.

For 100 business cards, the company charges $13. For 500 business cards, the company charges $33.

At this rate, what is the cost for 1,000 business cards?

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A. $53

B. $58

C. $66

17. For a special event, a restaurant charges a one-time setup fee, plus a charge for each person attending the event. The charge for 5 people is $100. The charge for 10 people is $162.50. How much is the one-time setup fee for an event?

A. $12.50

B. $16.25

C. $20.00

D. $37.50

18. The set of data in the table below represents a linear function.

x y

–6

–4

–2

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Which is an equation for this function?

A.

B.

C.

D.

19. The weights of two kittens were recorded on three consecutive days.

Part A Using data from the table, determine the rate of change of Rascal’s weight.

Part B Write a linear equation based on the data to model Rascal’s weight, y, after x days.

Part C Using data from the table, determine the rate of change of Snowball’s weight.

Part D Write a linear equation based on the data to model Snowball’s weight, y, after x days.

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Part E Solve the system of equations algebraically to determine the number of days before the kitten weights will be the same.

20. Which is an equation of the line that has a slope of 2 and passes through the point (3, 1)?

A. y = 2x + 5

B. y = 2x + 1

C. y = 2x – 1

D. y = 2x – 5

21. Which equation represents the data in the table below?

x y–3 –3–2 1–1 5

A. y = 2x + 3

B. y = 2x + 9

C. y = 4x + 3

D. y = 4x + 9

22. Jeana graphs the information from one of her monthly electricity bills.

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This bill is representative of the charges from other months throughout the year. The graph below shows the amount charged monthly in relation to the electricity used according to Jeana’s electricity bill.

Which statement is true of Jeana’s monthly electricity bill?

A. For every 15 units of electricity used monthly, the charge is $0.10.

B. For each unit of electricity used, the charge is $10 plus $15 for the first month.

C. Jeana has to pay $15 for each unit of electricity used and a $0.10 fixed monthly charge.

D. Jeana has to pay $1 for every 10 units of electricity used plus a $15 fixed monthly charge.

23. During a science experiment, the temperature of a liquid in a beaker started at 8°C and dropped by 0.8°C every 2 minutes.

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Which function models the temperature of the liquid, y, after x minutes?

A. y = 2.5x − 8

B. y = 0.5x − 8

C. y = 8 − 0.4x

D. y = 8 − 2.5x

24. Which is an equation of a line that goes through the point (2, 2) and has a y-intercept of 6?

A. y = 6x – 10

B. y = 2x + 6

C. y = –2x + 6

25. A fitness club charges $25 per month as well as a one-time $80 fee of all new members. Which equation represents the cost in dollars, , for a new member who prepays for months?

A.

B.

C.

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D.

26. An air conditioning company charges a flat fee for each service call, plus an hourly rate for any work completed. The table below shows the total cost for certain jobs based on the hours worked.

Hours Worked

Total Cost

3 $169.966 $289.93

10 $449.89

Based on a linear model, what does the company charge for a service call?

A. $39.99

B. $44.99

C. $49.99

D. $56.99

27. A car is traveling at a constant speed. The table below represents the time it takes the car to travel several distances.

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What does the slope represent in terms of given context?

A. The car is traveling 30 minutes per mile.

B. The car is traveling 2 minutes per mile.

C. The car’s speed is 30 miles per hour.

D. The car’s speed is 2 miles per hour.

28. The graph below represents the relationship between the time and distance a train traveled.

According to the graph, what is the average speed of the train in miles per hour?

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A. 150

B. 100

C. 75

D. 50

29. Which is an equation of a line with a y-intercept of –1 and goes through the point (–1, 1)?

A. y = –2x – 1

B. y = –x – 1

C. y = 2x – 1

30. The scatter plot below shows the relationship between students’ Algebra quiz scores on a 20-point quiz and the number of minutes each student watched television the evening before the quiz. An approximate line of best fit is shown for the data.

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Part A What is the y-intercept of the line of best fit?

Part B Explain what the y-intercept of the line of best fit represents for this context.

Part C What is the slope of the line of best fit?

Part D Explain what the slope of the line of best fit represents for this context.

31. Which is an equation of the linear function that passes through the points shown in the table below?

x y–2 –2–1 00 2

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1 4

A.

B.

C.

D.

32. Amanda bought sunflower bird seed for $2.39 per pound and millet bird seed for $2.99 per pound. She bought a total of 19 pounds of seed and paid $49.61.

Let f represent the number of pounds of sunflower seed and m represent the number of pounds of millet seed.

Part A Write an equation to represent the total pounds of seed Amanda bought.

Part B Write an equation to represent the total cost Amanda paid for the seed.

Part C Solve the system of equations to determine f, the number of pounds of sunflower seed, and m, the number of pounds of millet seed, Amanda bought. Show your work.

33. A linear graph of the function f(x) passes through the ordered pairs (2, 3) and (5, 4). What is the equation of f(x)?

A.

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B.

C.

D.

34. Which is an equation of the line that passes through the points (–

1, 1) and (4, –3)?

A.

B.

C.

D.

35. Which situation is modeled by the equation y = −15x + 300?

A. Maria has $300 in an account and deposits $15 each week.

B. A car uses 15 gallons of gas to travel a total distance of 300.

C. There are 300 people at a football game and 15 of the people leave the game each hour.

D. A scuba diver starts 300 feet below the water’s surface and dives

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down another 15 feet every minute.

36. A repairman charges a flat fee of $50 to come to a customer’s house, plus a charge per hour for any work completed. The repairman charged a customer $154 after 4 hours of work. Which function will calculate the cost of the repairman after x hours of work?

A. y = 26.00x + 50

B. y = 38.50x + 50

C. y = 50.00x + 26

37. Paula runs a bakery. She estimates that her weekly cost of rent and electricity is $250. The ingredients to bake one cake cost $4. Which equation represents the total cost to Paula’s bakery per week, y, if x number of cakes are made?

A.

B.

C.

D.

38. The table below represents the relationship between the weight of the human body and the weight of the human brain.

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Part A. Write a function to represent the brain’s weight (y) in terms of the body weight (x).

Part B. Find the slope of the function in part A and interpret it in terms of brain weight to body weight.

Part C. Find the y-intercept of the function in part A and interpret it in terms of brain weight to body weight.Part D. If the average weight of a person is 185 pounds, what is the weight of that person’s brain?

Use words, numbers, and/or pictures to show your work.

39. Which equation is a line that passes through the points (4, 5) and (0, –3)?

A.

B.

C.

D.

40. Kevin earns $250 per week, plus a 5% commission on all the furniture he sells, x. Which equation represents Kevin’s weekly income, y?

A. y = 255x

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B. y = 0.05 + 250x

C. y = 0.05x + 250


x y–4 –7–2 –60 –52 –44 –3


A.

B.

C.

D.

42. Carla put a new plant in her garden. She recorded the height of the plant, in centimeters (cm), every other day in the table below.

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Which statement best describes the relationship shown in the table?

A. The plant was 8 cm tall when planted and grew an average of 5 cm each day.

B. The plant was 4 cm tall when planted and grew an average of 5 cm each day.

C. The plant was 5 cm tall when planted and grew an average of 8 cm each day.

D. The plant was 5 cm tall when planted and grew an average of 4 cm each day.

43. Every visitor at a fair had to pay an entrance fee plus an additional cost per ride. Each ride at the fair costs the same. The table shows the total money spent, y, in dollars by a visitor who rode x different rides one time each.

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Part A Write an equation to represent the linear relationship between x and y. Show your work.

Part B Explain what the rate represents in this situation.

Part C Explain what the initial value represents in this situation.

44. The cost to join a gym includes a one-time membership fee, plus a monthly fee.

John joined the gym and paid $325 for 6 months. Abigail joined the gym and paid $475 for 9 months.

What is the monthly fee after a person joins the gym?

A. $25

B. $50

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C. $55

D. $150

45. A train traveling at a constant speed covers 320 miles in 4 hours. What equation can be used to model the distance, d miles, the train travels in time, t hours?

46. Which equation fits the data in the table below?

x y

2 6

4 8

10 14

A. y = 3x

B. y = 2x + 2

C. y = x + 4

47. Look at the graph.

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Part A. Write an equation that models the linear relation in the graph.

Part B. Write an equation for a line with the same slope that passes through the point


48. Which equation contains the coordinates (–1, 6) and (1, 2)?

A. y = –4x + 10

B. y = –4x + 2

C. y = –2x + 8

D. y = –2x + 4

49. Miriam saved an initial amount of money to buy a concert ticket. She continued to save a fixed number of dollars each week. The table represents the amount of money Miriam had saved at the end of weeks 3 and 7.

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Part A What is the rate of change for the data in the table?

Part B What does the rate of change represent in this situation?

Part C What was the initial amount of money Miriam had already saved? Show or explain your work.

50. Which is an equation of the line that passes through the points (2, 3), (6, 7), and (8, 9)?

A. y = 2x + 1

B. y = 2x − 1

C. y = x − 1

D. y = x + 1

51. The graph of the linear function g(x) is shown.

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Which equation has the same rate of change as g(x)?

A.

B.

C.

D.


x y–2 15–4 23–5 27


A.

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B.

C.

D.

53. Albert had $120 in his saving account on the first day of the year. He deposited some money at the end of January and decided to deposit the same amount at the end of every month. Albert has $300 in his account after 3 months. Which equation represents his savings, S, after m months?

A.

B.

C.

D.

54. Which equation, when graphed, will be a line that passes through all the points in the table below?

x y1 33 45 57 6

A. y = 0.5x + 2.5

B. y = x + 2

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C. y = 1.5x + 1.5

D. y = 2x + 1

55. A teacher has 75 books in his classroom collection. He bought 2 books in January, 2 books in February, and 2 more in March to add to his collection. If he continues adding to his collection each month in the same way, which function can he use to find n, the total number of books in his classroom collection after m months?

A.

B.

C.

D.

56. A t-shirt printing company charges a one-time setup fee, plus a charge to print each t-shirt. The math club had 75 t-shirts printed for a cost of $424. The science club had 50 t-shirts printed for a cost of $299. What is the cost of having 150 t-shirts printed?

A. $749

B. $799

C. $849

D. $899

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57. The salaries for the agents at an insurance company include a fixed base plus commissions on each policy sold. The table below shows the weekly salary for one agent.

Which statement is true for the function described in the table?

A. The slope shows that the agent earns $6 as commission on each sale while the initial value shows that his fixed base is $60.

B. The slope shows that the agent earns $60 as commission on each sale while the initial value shows that his fixed base is $6.

C. The slope shows that the agent earns $0.16 as commission on each sale while the initial value shows that his fixed base is $36.

D. The slope shows that the agent earns $36 as commission on each sale while the initial value shows that his fixed base is $0.16.

58. A veterinarian plans to put a dog on a diet plan for ten weeks so the dog’s weight decreases by the same number of pounds per week. The table shows how much the dog should weigh at different times on the diet plan.

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Based on the data in the table, what is the dog’s initial weight in pounds?

A. 99

B. 97

C. 95

D. 93


x y3 –56 –39 –112 1


A.

B.

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C.

D.


x y

What is the equation for this function?

A.

B.

C.

D.

61. This graph shows the change in elevation during Lynn’s hike.

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Based on the graph, what was the average rate of change in elevation in feet per hour?

A. 200

B. 300

C. 1,700

D. 3,000

62. Ten years ago the price of a 16-ounce bag of potato chips was $3.44. The current price of the 16-ounce bag is $4.74.

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Part A Using the values from the table, write a linear equation to model the price of potato chips. Show or explain all the steps you used to determine the equation.

Part B What does the slope of the linear equation represent in the context of this situation?

63. Which is an equation of the line that passes through the points (–

4, –4) and (4, –8)?

A.

B.

C.

D.

64. The scatter plot shows the relationship between the number of swimming lessons some students took and the number of seconds it took each student to swim across a 25-meter pool. An approximate line of best fit is shown for the data.

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Part A What is the y-intercept of the line of best fit?

Part B What is the slope of the line of best fit?

Part C The swimming instructor wants to know how the time it takes a student to swim across the pool is expected to change for every lesson taken. Does the instructor want to know the slope, y-intercept, or outliers? Explain your answer.

65. Which is an equation of the relation shown in the table below?

r s–2 1–1 20 31 42 5

A. r = 3s

B. r = s + 3

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C. s = 3r

D. s = r + 3

66. Isaac went on a bicycle trip from City A to City B and then bicycled back to City A along the same route. On the bicycle trip from City A to City B, Isaac rode his bicycle for a total of 3 hours. When Isaac bicycled back to City A, his average speed was 10 miles per hour slower and he rode for a total of 5 hours.

Part A Let d represent the distance, in miles, of each leg of Isaac’s bicycle trip. Let r represent Isaac’s average bicycle speed for the trip from City A to City B. Write a system of equations to represent Isaac’s bicycle trip from City A to City B and his trip back to City A along the same route.

Part B Fill in the table of values for each part of the trip.

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Part C What were Isaac’s two average speeds, in miles per hour? Make sure to specify which average speed is for Isaac’s bicycle trip from City A to City B and which average speed is for his trip back to City A along the same route. Explain how to find the average speeds using the table of values.

67. A company charges a standard delivery charge for book shipments as shown in the graph.

Based on the graph, which statement is not true about how the standard delivery charge is calculated?

A. The total charges always include a $3 fixed fee.

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B. The total charges for 2 books are calculated by doubling $1.50 and adding in a fixed fee.

C. The total charges always include a fee of $1.50 per book.

D. If the total charges are $12, divide this amount by the number of books shipped to find the fixed fee per book.

68. A table of x- and y-values of a linear function is shown below.

Which statement is true about the relationship between each pair of x- and y-values?

A. The y-values are one-half the value of the corresponding x-values.

B. The y-values are twice the value of the corresponding x-values.

C. The y-values decrease by 2 as the corresponding x-values increase by 1.

D. The y-values increase by 2 as the x-values increase by 1.

69. Which equation represents the data below?

x y–1 –3.70 –1.7

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1 0.32 2.33 4.34 6.3

A. y = –2x − 1.7

B. y = –2x + 1.7

C. y = 2x − 1.7

D. y = 2x + 1.7

70. Which is an equation of the line that goes through the points (–2, –

2) and (1, 7)?

A.

B.

C.

D.

71. Which is an equation of the line passing through the points (–2, –5) and (1, 4)?

A.

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B.

C.


x y

–2 7

–1 8

1 10

2 11


A. y = –3x + 1

B. y = x + 9

C. y = 5x + 1

73. The table represents the relationship between the values for x and y.

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Which function represents the relationship between the x-values and the y-values shown in the table?

A.

B. f(x) = 2x + 5

C. f(x) = 4x + 3

D. f(x) = 5x + 2

74. The graph below shows a linear relationship. The points shown have whole-number coordinates.

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Which function models the linear relationship shown on the graph?

A.

B.

C.

D.

75. Water Fun Plus charges customers $50 per day to rent a canoe and $25 as a nonrefundable insurance fee.

Part A. Write a function that represents the total cost y of renting a canoe for x days at Water Fun Plus.

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Part B. What do the slope and y-intercept in the function for Water Fun Plus represent in terms of the context?

Part C. Make a table of x and y values to show the cost of renting a canoe at Water Fun Plus for the first 5 days. Use this table to determine whether the function is linear. Explain how you know whether or not the function is linear.

Part D. Another company, Outdoor Adventures, charges $70 per day to rent a canoe, but with no insurance fee. Write a function to model the total cost y of renting a canoe for x days at Outdoor Adventures. Explain how this function compares to the function written in part A for Water Fun Plus.


76. Which equation is a line that passes through the point (–4, –4) and has a y-intercept of 2?

A.

B.

C.

D.

77. Which is an equation of a line that passes through the points (–3, 3) and (2, 8)?

A. y = x + 6

B. y = 2x + 3

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C. y = 2x + 8

78. Sean and Julie are landscapers. Each person charges a one-time fee plus an hourly fee. Sean uses the equation to determine the charge, y, in dollars for working x hours. Julie uses this table to determine the charge, y, for working x hours.

Which statement is true for these two landscapers?

A. Sean charges a greater one-time fee because the equation shows a greater rate of change than the table.

B. Julie charges a greater one-time fee because the table shows a greater rate of change than the equation.

C. Sean charges a greater one-time fee because the equation shows a greater y-intercept than the table.

D. Julie charges a greater one-time fee because the table shows a greater y-intercept than the equation.

79. In 2007, the population of a town was approximately 35,250. In 2012, the population of the town had decreased to 28,200. Based on a linear model, what will be the approximate population of

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the town in 2014?

A. 31,020

B. 26,800

C. 25,380

D. 15,510

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

A.

B.

C.

D.

81. Two panda bear cubs’ weights were recorded on three different days.

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Part A Using the data from the table, determine the rate of change of Panda W’s weight. Show your work.

Part B Write a linear equation based on the data to model Panda W’s weight, y, after x days.

Part C Using data from the table, determine the rate of change of Panda Z’s weight. Show your work.

Part D Write a linear equation based on the data to model Panda Z’s weight, y, after x days.

Part E Solve the system of equations algebraically to determine the number of days before the panda cubs’ weights will be the same. Round your answer to the nearest day. Show your work.

82. Use the graph below to answer the question.

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Which statement is true about Connie’s savings account?

A. Connie started with $25 in her savings account and saved $40 each week.

B. Connie started with $25 in her savings account and saved $15 each week.

C. Connie started with $15 in her savings account and saved $25 each week.

D. Connie started with $0 in her savings account and saved $25 each

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week.

83. The value of a car over a period of time is shown in the table below.

Which statement is true of the value of the car?

A. The initial value of the car is $15,000, and it increases by $750 every year.

B. The initial value of the car is $16,500, and it increases by $750 every year.

C. The initial value of the car is $15,000, and it decreases by $750 every year.

D. The initial value of the car is $16,500, and it decreases by $750 every year.

84. Which is an equation of a line that passes through the points (–2, –

1) and (3, 4)?

A. y = –2x – 1

B. y = x + 1

C. y = 2x – 2

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85. A linear equation is modified so that the rate of change is tripled, but the y-intercept remains the same. Which pair of equations could represent the original equation and the modified equation?

A. y=x+3 and 3y=3x+9

B. y=9x−2 and y=12x−2

C. y=−2x−3 and y=−2x−9

D. y=−5x+6 and y=−15x+6

86. Which is an equation of a line with a slope of 2 and goes through the point (0, 3)?

A. y = 2x + 3

B. y = 3x + 2

C. y = 5x

87. Which is an equation of a line with a slope of 5 and goes through the point (1, 4)?

A. y = –x + 5

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B. y = 5x – 1

C. y = 5x + 4

88. A swimming pool is being drained. The table below shows the volume of water, y, in cubic feet, after x minutes of draining.

Which equation can be used to model the function shown in the table?

A.

B.

C.

D.

89. The graph below models the costs of renting video games, including the cost of an initial membership fee, at a video game store.

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Which scenario best describes the graph?

A. The cost per video game is $10 with an initial membership fee of $2.

B. The cost per video game is $10 with an initial membership fee of $4.

C. The cost per video game is $2 with an initial membership fee of $10.

D. The cost per video game is $4 with an initial membership fee of $10.

8.F.4 /53

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