8.SP.3 [565814]StudentClassDate

1. A student bought two identical plants that are each 18 inches tall. The equation h=0.2w+18 can be used to represent both plants’ base growth rate, where h is the height, and w is the number of weeks of growth. On Plant 2, however, the student used fertilizer, which increased Plant 2’s weekly growth by 50%. Which equation gives the height of Plant 2 each week?

A.   h=0.3w+18

B.   h=0.3w+27

C.   h=0.5w+18

D.   h=0.5w+27

2. The graph shows the height of a plant over several weeks.

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Using a linear model, what is the approximate height of the plant after 14 weeks?

A. 11 in.

B. 14 in.

C. 17 in.

D. 21 in.

3. 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.

4. James asked six classmates about the amount of time they spend outside and the amount of time they spend watching TV on Saturday. He plotted the results on the graph below.

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Which is the best estimate for the amount of time someone spends outside if he or she watches 2.5 hours of TV?

A. 1.5 hours

B. 2 hours

C. 3 hours

D. 3.5 hours

5. To Build a Skyscraper

Construction of a new skyscraper in a large city began in 2006 and was completed in May 2013. The building was designed to have a windowless base that is 200 feet squared and 185 feet high. Above the base, there are the office floors, starting with the 20th floor. At the top of the building, there is a large spire, which was the last part of the skyscraper that was

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constructed.Part A. The table below shows the progress in the construction of the skyscraper, from the pouring of concrete into the foundation 80 feet below the surface to the placement of the spire. The final height of the building was 1,776 feet.

Study the growth of the building from February 2010 until the 100th floor was reached in March 2012. Using the numbers given, estimate the missing heights and fill in the table. Explain your work.

Part B. In the graph below, each unit on the x-axis represents one quarter of

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a year, or 3 months, beginning with November 2006. Plot the values from the table on the graph.

Part C. Determine the periods of time when the building had the slowest growth rate and when the building had the most rapid growth rate. Explain what was happening during these time periods, including how this relates to the slope of the graph at that time.Part D. Draw a line of best fit on your graph above for both periods of time listed in part C. Then, determine the slopes of these lines, showing all work. What do these slopes represent? Explain how they relate to your answers in part C.Part E. Write equations for the lines of best fit you drew in part D. Explain the meaning of the y-intercepts of both equations in terms of the context of this situation.

Part F. Explain why you think there were variations in the growth of the skyscraper as it was being built. Why isn't growth always constant? Refer to

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the equations you wrote in part E and the table in part A.

6. The graph shows the wolf population near a city.

Using a linear model, what is the best estimate of the wolf population in 2020?

A. 100

B. 400

C. 500

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D. 800

7. The scatterplot below represents the relationship between the total cost for plumbing service and the number of hours worked by plumbing companies in a city.

Using a linear model for the data, what was the approximate average hourly cost for services by plumbing companies in the city?

A. $100.00

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B. $75.00

C. $65.00

D. $40.00

8. The equation  can be used to predict the number of hours, y, it takes Zula to write x number of articles for a newspaper. Which of these is the best interpretation of the slope of this linear model?

A. Zula can write  articles in  hours.

B.Zula can write of an article in   hour.

C. It takes Zula  minutes to write each article.

D. It takes Zula  minute to write each article.

9. Tanya is growing her hair out. She records the length of her hair at the end of each month and plots the data in the graph below. The equation of a line that approximates the data is  .

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Assuming she does not cut her hair, about how long can Tanya expect her hair to be after 8 months?

A. 14 inches

B. 16 inches

C. 20 inches

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D. 28 inches

10. A scientist conducted an experiment on the effects of the height of corn after x amounts of fertilizer. The scatterplot below displays the heights (cm), y, of 3-week-old corn plants after x amounts (mg) of fertilizer were given to the plants.

Approximately, what was the height of a 3-week-old corn plant that received no fertilizer?

A. 0 cm

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B. 34 cm

C. 52 cm

D. 68 cm

11. The graph below represents the cumulative number of hours Jack slept during a week.

Using a linear model for the data, what is the meaning of the slope?

A. the amount of hours Jack slept per night

B. the amount of sleep Jack got the first night

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C. the amount of nights Jack slept per week

D. the number of hours Jack was awake

12. A scientist recorded the weight of an insect from hatching to maturity. The equation w=0.7a+1.2 gives the insect’s weight, w, in grams at age a, in weeks. What is the meaning of the slope of this equation?

A.   The weight of the insect increases 1.2 grams each week.

B.   The weight of the insect increases 0.7 grams each week.

C.   The weight of the insect is 1.2 grams when it hatches.

D.   The weight of the insect is 0.7 grams when it hatches.

13. A man used a faucet to add water to a pond. The man used the equation v=3,208m+6,000 to determine the volume, v, of the pond in milliliters after he had added water for m minutes. What is the meaning of the y-intercept of this equation?

A.   The volume of the pond increases by 3,028 milliliters each minute.

B.   The volume of the pond increases by 6,000 milliliters each minute.

C.   The volume of the pond was 3,028 milliliters before the water was added.

D.   The volume of the pond was 6,000 milliliters before the water was

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added.

14.

The equation for the height of a burning candle is where h represents the candle’s height in centimeters after elapsed time, t, in minutes. Which equation represents the height of a second burning candle that is 5 centimeters taller than the first candle?

A.

  

B.    

C.

  

D.   

15. The graph shows the amount of money that cheerleaders raised each week over a period of six weeks.

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Using a linear model, approximately how much money will the cheerleaders raise in week 7?

A. $40

B. $50

C. $60

D. $70

16. Savannah collected data to determine whether the time a student spends playing video games each week has any effect on the student’s math grade. She represented her data on a scatter plot. The equation for the line of best fit was where x represents the number of hours a student spent playing video games and y represents the student’s math grade. Which statement must be true?

A. Students who play video games have an average math grade of 97.5

B. Students who do not play video games have an average math grade of 91.5.

C. An increase of 6 hours per week spent playing video games is associated with a decrease of 1 point in a student’s math grade.

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D. A decrease of 1 hour per week spent playing video games is associated with an increase of 6 points in a student’s math grade.

17. A student had already read some pages in a book when he created the model below. The model tracks p, the total amount of pages read if the student reads for h hours.

Which statement best explains the meaning of the slope in this model?

A. The student tends to read 30 pages per hour.

B. The student tends to read 60 pages per hour.

C. The student will have 30 pages left to read after 1 hour of reading.

D. The student will have 60 pages left to read after half an hour of reading.

18. A server in a restaurant earns a fixed hourly salary plus tips, which depend on the bill amount of the meal he serves. He estimated that the average amount he earns in an hour can be modeled by the equation

where x is the total value of the meals he serves in an hour. Which statement represents the correct interpretation of this equation?

A. The slope represents that the server earns $8.65 as his fixed hourly salary.

B. The y-intercept represents that the server has $8.65 as his fixed hourly salary.

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C. The slope represents that the server’s tip is 15% of the value of the meals he serves in an hour.

D. The y-intercept represents that the server’s tip is 15% of the value of the meals he serves in an hour.

19. The equation y = 0.95x + 3 models the cost to ride in a taxi, where y is the total cost for a ride, and x is the number of miles driven. What does the slope of the line represent?

A. It costs $3.95 to ride in the taxi.

B. The flat fee to ride in the taxi is $3.

C. The cost per mile to ride in the taxi is $0.95.

20. The scatterplot below shows the relationship between years of experience on a job and the income earned at that job.

What is the relationship between years of experience and income earned?

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A. The income at 15 years and 25 years is the same.

B. The more years of experience a person has, the less the income.

C. The more years of experience a person has, the higher the income.

D. The income stays the same no matter how many years of experience.

21. When t is the time in hours, the equation  gives the total accumulated snow depth, d, in inches during a storm. Using this equation, how much snow will be added with each hour?

A.   1 inch

B.   2 inches

C.   8 inches

D.   10 inches

22. A family recorded and graphed the average temperature outside and compared it to the monthly heating bill each month.

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Based on this linear model, what is the expected heating cost if the average temperature outside was 35°F?

A. $75

B. $225

C. $350

D. $400

23. The scatterplot below shows the number of students receiving any type of financial aid at a school from 2000–2010.

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Based on the model, which is the best prediction for the number of students who will be receiving financial aid in 2013?

A. 200 students

B. 210 students

C. 225 students

D. 250 students

24. The graph below shows the owl population in a city over several

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years.

Using a linear model, which is the best estimate of the owl population in 2010?

A. 250

B. 320

C. 350

D. 40

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0

25. The scatter plot shows the altitude of an airplane during its descent. The equation of the line of best fit for the data shown on the graph is y=30,737−2,099x where y is the altitude in feet and x is the time in minutes.

Part A  What is the slope of the line of best fit and what does it represent in this situation?

Part B  What is the y-intercept and what does it represent in this situation?

Part C  What is the x-intercept and what does it represent in this situation?

26. The scatterplot below shows the effect the amount of light a plant receives each day has on the growth of the plant over a 30-

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day period.

Based on a linear model, about how tall would a plant be if it received 6 hours of light each day?

A. 8 cm

B. 12 cm

C. 14 cm

27. The scatterplot below shows the relationship between the money spent on groceries each week, x, and the amount of money spent eating out at restaurants, y, during that same week by six different families.

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Using a linear model for this scatterplot, what does the y-intercept represent?

A. the amount of money spent eating out if there are no groceries purchased

B. the amount of money spent on groceries when a family does not go out to eat

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C. the decrease in the amount of money spent eating out for each dollar spent on groceries

D. the increase in the amount of money spent eating out for each dollar spent on groceries

28. Tilda kept track of how long it took her to assemble various puzzles based on the total number

of puzzle pieces. She determined that the linear model can be used to estimate y, the total time, in minutes, it will take her to assemble a complete puzzle based on x, the total number of puzzle pieces. What does the slope in Tilda’s equation represent?

A.The initial hour needed to sort the puzzle pieces before assembling the puzzle.

B.The rate of minute per puzzle piece while assembling the puzzle.

C. The initial 5 minutes necessary to sort the puzzle pieces before assembling the puzzle.

D. The rate of 5 minutes per puzzle piece while assembling the puzzle.

29. The graph below shows the relation between the height from which a ball is released and the maximum height it reaches on its first bounce.

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What can be concluded from the line of best fit shown on the graph?

A. The bounce height is 0.5 inch less than the release height.

B. The bounce height is 2 inches less than the release height.

C. The bounce height is 0.5 times the release height.

D. The bounce height is 2 times the release height.

30. Puppy Math

Rhianna and Felipe each got a puppy. They both recorded the weight of their puppies twice a month for the first 6 months.

Part A. Rhianna has a cocker spaniel. Her puppy’s growth is shown in the chart.

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Plot the puppy’s growth on the graph.

 

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Part B. Felipe has a golden retriever. His puppy’s growth is shown in the chart. Plot the growth of his puppy using a different color on the same graph. Label the graph for each puppy.

 Part C. From looking at the graphs, what can you tell about the growth rates for the two puppies? Explain your answer.

Part D. If you drew a line through each set of the points on the graph, what would the slopes of the lines represent? What are the units?

How can you find the slope of a graph? In a situation like this where the slope changes from month to month, what is a good way to find the average slope?

To the nearest whole number, what is the average slope of the graph for Rhianna’s puppy? For Felipe’s puppy?

Part E. The points on these graphs do NOT form perfectly straight lines. What does that fact tell you about growth and measurement in the real world?

Part F. If you kept plotting the size of the dogs as they got older, would you expect these lines to keep going the same way indefinitely? Why or why not? If Felipe’s dog kept growing at the same rate as in the first 6

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months, about how much would it weigh by age 10?

Part G. What does the y-intercept of one of these graphs represent? Explain your answer.

Part H. At one year of age, Rhianna’s cocker spaniel weighed 26 pounds and Felipe’s golden retriever weighed 70 pounds. How do the dogs’ growth rates in the second half-year compare with their growth rates in the first half-year? Explain your answer.

31. The scatterplot shows the average amount of milk consumed by an adult over a 30-year period in the United States.

Based on the scatterplot, approximately what will be the consumption of milk for an adult in the year 2015?

A. 10 gallons

B. 15 gallons

C. 20 gallons

D. 25 gallons

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32. A restaurant manager compared the amount of time, y, in minutes, that a group waited to be seated and the number of people in the group, x, during the past several weeks. The line of best

fit for the data collected was . Based on the line of best fit, how much additional wait time, in minutes, is associated with each additional person in the group?

A. 11.5

B. 10

C. 3

D. 1.5

33. The graph shows Isabella’s savings account over several months.

Using a linear model, what is Isabella’s approximate balance in month 5?

A. $200

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B. $250

C. $300

D. $350

34. Emma bought a new plant. She recorded the growth of her new plant each week for 7 weeks. She created the scatterplot below with her data.

Based on a linear model, what does the slope represent?

A. The plant grows about 4 cm a week.

B. The plant grows about 10 cm a week.

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C. The plant was about 5 cm tall when Emma bought it.

35. Mr. Romario receives his monthly salary by direct deposit into his checking account. The scatterplot below displays his balance, y, after x days of making the deposit.

Using a linear model that most closely represents this data, what is the meaning of the slope?

A. The account decreased by $75 every 2 days.

B. The account decreased by $75 every

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day.

C. The account decreased by $80 every 2 days.

D. The account decreased by $80 every day.

36. Mandy kept track of the trade-in value of a collector’s coin for several months through February

of this year. She determined the line of best fit for the data was , where y is the trade-in value, in dollars, x months after February of this year. According to the equation, when will the trade-in value of the coin be $44?

A. October of the same year

B. December of the same year

C. April of the following year

D. June of the following year

37. The linear model   represents the number of pairs of sandals sold, y, for a given outdoor temperature of x degrees at a certain shoe store. How many pairs of sandals should the company expect to sell if the outside temperature is 90 degrees?

A. 45 pairs

B. 54 pairs

C. 90 pairs

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D. 99 pairs

38. The scatterplot below shows the heights, x, and weights, y, of several dogs in a kennel.

Which describes the slope of the line that best fits this data?

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A. The smallest dog is 5 inches tall and weighs about 8 pounds.

B. The height of a dog increases about 2 inches for each additional pound.

C. The average weight of a dog decreases for each additional inch of height.

D. The average weight of a dog increases about 2 pounds for each additional inch of height.

39. A reporter collected data about the price of gasoline during the first 16 weeks of 2012. The equation  models the relationship between p, the price of a gallon of gasoline in dollars, and w, the number of weeks after January 1, 2012. According to this model, by how much did the price of a gallon of gasoline increase each week?

A. $0.0423

B. $0.6768

C. $3.2863

D. $3.3286

40. The scatterplot below shows the effect the weight of a car has on its gas mileage.

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Using a linear model, about how many miles per gallon will a car get that weighs 4,500 pounds?

A. 8 miles per gallon

B. 10 miles per gallon

C. 13 miles per gallon

41. Taylor planted a seedling and measured its height each day. Her results are recorded in the graph below.

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Using a linear model, approximately how tall will the seedling be in 20 days?

A. 16 cm

B. 14 cm

C. 12 cm

D. 9 cm

42. The scatterplot below displays the number of miles, y, Jackson ran over several weeks, x, while he was training for a competition.

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Which statement describes the y-intercept?

A. the number of miles Jackson ran after one week of training

B. the number of miles Jackson ran before starting his training

C. the increase in the miles Jackson ran each week

D. the decrease in the miles Jackson ran each week

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