School Name:

Teacher Name:

Student Name:

8.F.B.4

Subject: Mathematics

State: Tennessee

2 A student has had a collection of baseball cards for several years. Suppose that  , the number of baseball Bcards in the collection, can be described as a function of  , which is the time in years since the collection was tstarted. Explain what each of the following equations would tell us about the number of cards in the collection over time.

(a) = 200 + 100 B t

(b) = 100 + 200 B t

(c) = 2000 − 100 B t

(d) = 100 − 200B t

1 Juan had a checking account with a balance of dollars. After he withdrew dollars, he had a balance x yof $100. Which of the following shows the correct relationship between , , and $100?x y

= $100(A) x − y 

$100 < (B) x − y

+ = $100(C) x  y 

> $100(D) x − y 

3 You have $100 to spend on a barbecue where you want to serve chicken and steak. Chicken costs $1.29 per pound and steak costs $3.49 per pound.

(a) Write a function that relates the amounts of chicken and steak you can buy.

(b) Graph the function you wrote in part (a). What is the meaning of each intercept in this context? What is the meaning of the slope?

(c) Use your graph, the information in part (b), and any other information from the equation and graph, to discuss what your options are for the amounts of chicken and steak you can buy for the barbecue.

4 A car is traveling down a long, steep hill. The elevation,  , above sea level (in feet) of the car when it is E d miles from the top of the hill is given by the equation  = 7500 − 250 , where  can be any number from 0 E d dto 6.

Find the slope and intercepts of the graph of this function and explain what they mean in the context of the moving car. 

6 Which of the following scenarios could be modeled by the equation  = 2 + 5? Circle YES or NO for y xeach one.

(a) There are initially 5 rabbits on the farm. Each month thereafter the number of rabbits is 2 times the number in the month before. How many rabbits are there after months?x

          YES or NO

5 The total cost of an order of shirts from a company consists of the cost of each shirt plus a one-time design fee. The cost of each shirt is the same regardless of how many shirts are ordered.

The company provides the following examples to customers to help them estimate the total cost of an order of shirts.

50 shirts cost $349.50.

500 shirts cost $2370.

(a) Based on the examples, what is the cost of each shirt, including the one-time design fee? Explain how notyou found your answer.

(b) What is the cost of the one-time design fee? Explain how you found your answer.

(b) Joaquin earns $2.00 for each magazine sale. Each time he sells a magazine he also gets a five-dollar tip. How much money will he earn after selling magazines? x

          YES or NO

(c) Sandy charges $2.00 an hour for babysitting. Parents are charged $5.00 if they arrive home later than scheduled. Assuming the parents arrived late, how much money does she earn for hours?x

          YES or NO

(d) I have a sequence of integers. The first term of the sequence is 7 and the difference between any consecutive terms is always equal to 2.

          YES or NO

(e) Sneak Preview is a members-only video rental store. There is a $2.00 initiation fee and a $5.00 per video rental fee. How much would John owe on his first visit if he becomes a member and rents videos? x

          YES or NO

(f) Andy is saving money for a new CD player. He began saving with a $5.00 gift and will continue to save $2.00 each week. How much money will he have saved at the end of weeks? x

          YES or NO 

7 A trainer for a professional football team keeps track of the amount of water players consume throughout practice. The trainer observes that the amount of water consumed is a linear function of the temperature on a given day. The trainer finds that when it is 90°F the players consume about 220 gallons of water, and when it is 76°F the players consume about 178 gallons of water.

Write a linear function to model the relationship between the gallons of water consumed and the Part A:temperature.

Part B: Explain the meaning of the slope in the context of the problem.  

9 In science class, Mrs. Winkler's students are studying the water flow in a channel close to their school. A cross section of the channel approximates the shape of an isosceles trapezoid with dimensions noted on the diagram below.

8 The prices and sizes of several houses for sale in a neighborhood are shown in thescatter plot below.

Which equation represents the line of best fit?

y = 100x(A)

y = 100x + 50,000(B)

y = 1,000x(C)

y = 1,000x + 50,000(D)

The students found that there is a linear relationship between the and the water depth distance across the . This means that we can write , the distance across the channel at water level (in feet), channel at water level y

as a function of the water depth, (in feet).d

(a) Use the information found in the diagram to find two depth-distance pairs ( , ) that correspond with d yeach other. In other words, find two input-output pairs for the function.

(b) Find an equation that describes as a function of . Draw the graph of the equation.y d

(c) Explain the meaning of the slope and the vertical intercept of the line in the context of the situation. In other words, what does each tell you about the depth of the water and the distance across the channel at water level?

(d) What is the distance across the channel at water level when the water is 2 feet deep?

(e) Formulate and answer another question about this situation.

10 Serena is starting a new workout routine and wants to keep track of her heart rate to make sure that she is exercising at the optimum level. First she did a warm-up, then she did her training exercises, then she did a cool-down.

Before beginning her workout, Serena's heart rate was 60 beats per minute.

She started her workout with a warm-up. While warming up, her heart rate increased at a constant rate of 8 beats per minute each minute.

She warmed up for 10 minutes.

After her warm-up, her heart rate held steady throughout her training exercises, which lasted for 30 minutes.

After her training exercises, she walked for 20 minutes as a cool-down and her heart rate decreased at a constant rate, finally returning to her rest rate of 60 beats per minute by the end of her cool-down.

(a) Construct a graph of Serena's heart rate, , in beats per minute (bpm), as a function of time, , in minutes, h twhere = 0 is when she started her warm-up. Make sure to include the times before, during, and after her tworkout.

(b) For about how many minutes total was her heart rate at 100 beats per minute or above? Explain.

(c) Compare how quickly her heart rate changed during her warm-up versus how quickly her heart rate changed during her cool-down. Explain.

11 Joshua's mail truck travels 14 miles every day he works, and is not used at all on days he does not work. At the end of his 100th day of work the mail truck shows a mileage of 76,762.

= [ ] + ]. y blank 1 x [blank 2 (a) Find values of and to express the mileage as a linear function in the m b yform  of the number of days that Joshua has worked. Explain your answer.y = mx + b x

For parts (b) and (c), choose from the following options:

days

miles

days/mile

miles/day

There is not enough information to tell.

(b) What are the units on the slope from your answer to part (a)? m

(c) What are the units on the -intercept from your answer to part (b)? y b

For parts (d) and (e), choose from among the following options:

The mileage at the end of Joshua's first day of work.

The number of miles Joshua drives the truck each day he works.

The mileage at the beginning of Joshua's first day of work.

The number of days Joshua works for each mile he drives.

The number of miles Joshua drives at work over 100 days.

12 Carmella graphed line on the coordinate grid shown below.p

Which of the following lines appears to have the same slope as line ?p

(d) Which of the options is the correct interpretation of the slope, , in your equation in part (a)? Select all mcorrect answers.

(e) In this context, which of the options is a correct interpretation of the -intercept, , in your equation in y bpart (b)? Select all correct answers.

(A)

(B)

(C)

(D)

13 Some of the students from Eastwood School are taking a trip to a museum. In all, fewer than 60 students will go on the trip. The cost for food and admission to the museum is $18 per student.

(a) What is the total cost for food and admission to the museum for 15 students? Show or explain how you got your answer.

The students will travel on one bus to the museum. The cost of the bus is $800.

(b) Complete the table below to show the total cost for food, admission, and the bus for different numbers of students to go to the museum. Show or explain how you got your answers.

(c) Write an expression that can be used to find the total cost for food, admission, and the bus for students nfrom Eastwood School to go to the museum.

(d) A total of 44 students go to the museum. What is the total cost, for food, admission, and the bus, per to go to the museum? Show or explain how you got your answer.student

14 A pool cleaning service drained a full pool. The following table shows the number of hours it drained and the amount of water remaining in the pool at that time.    Pool Draining

Time (hours) 3 5 7 9 11

Water Remaining(gallons) 

13,200 12,000 10,800 9,600 8,400

     Part A    Plot the points that show the relationship between the number of hours elapsed and the number of gallons of water left in the pool. 

Part B    The data suggest a linear relationship between the number of hours the pool had been draining and the number of gallons of water remaining in the pool. Assuming the relationship is linear, what does the rate of change represent in the context of this relationship?     A. The number of gallons of water in the pool after 1 hour.    B. The number of hours it took to drain 1 gallon of water.    C. The number of gallons drained each hour.    D. The number of gallons of water in the pool when it is full.   

Part C   

What does the -intercept of the linear function represent in the context of this relationship?y    A. The number of gallons of water in the pool after 1 hour.    B. The number of hours it took to drain 1 gallon of water.    C. The number of gallons drained each hour.    D. The number of gallons of water in the pool when it is full.   

Part D    Which equation describes the relationship between the time elapsed and the number of gallons of water remaining in the pool?     A. = -600 + 15,000y x    B. = -600 + 13,200y x    C. = -1,200 + 13,200y x    D. = -1,200 + 15,000y x

15 Juan purchased one binder for $3.50 and f folders for $1.25 each. The total cost, C, in dollars, of Juan’s purchase is represented by the equation below.

C = 3.50 + 1.25f

Which of the following graphs represents , the total cost of Juan’s purchase if he buys different numbers of Cfolders?

(A)

(B)

(C)

(D)

16 The graph below shows the temperature, in degrees Fahrenheit, of a liquid for the first ten minutes of a heating experiment.

Based on the graph, which expression could be used to calculate the temperature of the liquid after mminutes?

5 + 40(A) m

−5  − 40(B) m

10 + 40 (C) m

−10  − 40 (D) m

17 The graph below shows the relationship between the distance a delivery truck is driven and the amount of gas the truck uses.

Based on the graph, what is the average distance, in miles, the truck can be driven using 1 gallon of gas?

10(A)

12(B)

14(C)

16(D)

18 The table below shoes the cost of different numbers of goldfish at a pet store.

The cost is a linear function of the number of goldfish. Which statement describes the rate of change of this function?

The cost increases $0.30 each time 1 goldfish is added.(A)

The cost increases $1.50 each time 1 goldfish is added.(B)

The cost increases $3.00 each time 5 goldfish are added.(C)

The cost increases $6.00 each time 5 goldfish are added.(D)

19 The graph below shows the number of calories Benjamin will burn over time while walking at a constant rate

Based on the graph, what is the number of calories Benjamin will burn after walking at a constant rate for 42 minutes?

132(A)

162(B)

168(C)

210(D)

20 A company makes hats with custom designs. For each custom order, the company charges a one-time fee of $25.00 for the design and $12.50 for each hat made.

Write an equation that can be used to find , the total cost, in dollars, of a custom order, in terms of , the c hnumber of hats made.

21 What is the slope of the line graphed below?

23 A customer is comparing two different text message plans at Cellular Bargains. He wants to find out which plan allows the most text messages for the same cost. 

 The Pay Per Text Plan charges $10 per month and $0.10 for each text message. Write a function that models this plan, stating what your variables represent.    The Frequent Text Plan is modeled by the graph shown below.

22 What is the slope of the line represented by the equation below?

4  + 5  = 10x y

(A)

− (B)

4(C)

−4(D)

45

45

How many text messages would result in the same cost per month for the two plans?          

24 The cost to rent a paddleboat at the city park includes an initial fee of $7.00, plus $3.50 per hour. Which equation models the relationship between the total cost, y, and the number of hours, x, that the paddleboat is rented?

(A) y = 3.5x + 7

(B) y = 7x + 3.5

(C) y =   + 3.5

(D) y =  + 7

x7

  x3.5

25 A tank of water was drained at a constant rate. The table shows the number of gallons of water left in the tank after being drained for two amounts of time.

What is the rate at which the water was drained from the tank?

6 gallons of water per minute(A)

11 gallons of water per minute(B)

45 gallons of water per minute(C)

120 gallons of water per minute(D)

26 A tank of water was drained at a constant rate. The table shows the number of gallons of water left in the tank after being drained for two amounts of time.

What was the total amount of water in the tank before it was drained?

450 gallons(A)

510 gallons(B)

560 gallons(C)

570 gallons(D)