Activities

1. The best-fit line for a set of data is y = 0.05x + 20. Predict the output if the input was 50.

2. Draw a best-fit line through the data displayed below.

3. The scatterplot below displays the amount of money in Willie’s bank account each month this year. Approximately how much did he have in savings at the start of the year and how much is his account growing per month?

4. The best fit line m = 25g + 5 represents the number of miles (m) a car can be driven based on the number of gallons of gas (g) you buy at the gas station. How many miles could you travel if you purchased 7 gallons of gas?

5. The scatterplot below portrays the amount of money in Frank’s college book fund since the beginning of the semester. Estimate how many months from the beginning of the semester until Frank runs out of money.

6. The best fit line for the height of a corn plant (h) based on the number of days since planting (d) is h = 0.75d – 5. Why is the y-intercept of this equation negative?

7. The best fit line for the number of days (d) it takes a certain video gamer to beat various levels (L) on a new video game is L = 0.25d + 1. About how many days does it take for the player to beat each level?

8. Katee has been tracking the number of songs she has downloaded on her smart phone for the past several months. Use the scatterplot and line of best fit below to help her determine when she will reach 10,000 songs?

9. Laura has been tracking the weight of her Rottweiler puppy, Duke, for a number of months. She plotted her data here. What is the expected weight of Duke in May?

10. Saleemah has been trying to practice for the upcoming ACT test. She has been completing a practice version of the test each weekend and tracking her data as she improves. A scatterplot of the percentage of questions she did not attempt because she ran out of time for each practice test is shown below. How many more practice tests should Saleemah take in order to try all of the problems.

11. All of the chickens in a hen house lay their eggs according to the best-fit equation e = 247d + 11 where there are a number of eggs (e) based on the number of days (d). How many hens are in the hen house if each chicken lays 0.75 eggs per day?

12. The battery life on your cell phone decreases according to the scatterplot below. What is the longest amount of time you could use your phone without charging it?

13. The line of best fit for number of fans attending a baseball teams home games looks like this. If this trend continues, how many spectators will be there at game number ten?

14. A line of best fit that inputs the height (h) of a building, in feet, and outputs the number of floors (f) in the building is generally . Use the equation to find the height of a building with 24 floors.

15. What is your best prediction of the next coordinate point in this set of data?

16. Scott has been keeping data on himself regarding how many hamburgers he eats per week. He plotted the data and created a best-fit equation of h = 10w + 1, where h is the number of hamburgers eaten and w is the number of weeks since he started keeping track. What would be the best-fit equation of the number of hamburgers (h) eaten per day (d)?

17. Tim eats pancakes every morning according to the best-fit equation p = 3.5d + 30 where p is the number of pancakes eaten after some amount of days (d). Why does the solution (1, 33.5) not make sense in this equation?

18. Nick and Luke have been tracking the progress of their grades over the past several months. Compare the two scatterplots, with their line of best fit, below, describing what you think the R² value means.

19. The scatterplot below shows the coordinate points of the equation y = x². Additionally, it displays the line of best fit for this graph. Explain why the line will not fit well as it continues into higher values.

20. Very rich individuals gain their wealth through interest. This is because to gain wealth in a linear fashion would take too much time. For instance, the median salary in the US in 2014 is $52,000. How many years of earning $52,000 would an employee have to work in order to earn $1,000,000?

21. Estimate where the next point would be on the following graph?

22. A man’s salary doubles each month. Why would a linear line of best fit not describe that data well? What would be a better function to fit that data?

23. Create a scatter plot of distance versus time, which would go through the point (15, 35).

24. Predict the equation for a line of best fit that inputs the number of hours a person walks and outputs the number of miles they still need to cover from Philadelphia to Pittsburgh.

25. The line of best fit for the number of pages (p) Shakira read in a large novel based on the number of hours (h) she had spent reading was: p = 18h + 16. Determine the integer values for h when she had read 144, 365 and 499 pages?

Answer Key/Rubric

1. 22.5
   
   
2. 
   
   

3. Started with 30 and the account grows by $101 per month.

4. 180 miles

5. He will run out of money 3.66 months into the semester

6. The y-intercept is negative because it takes 5 days for the corn to come up through the dirt

7. Approximately 4 days per level

8. 398 weeks

9. 52 pounds

10. 3 more tests

11. About 329 chickens

12. 16.67 hours

13. 21,600 spectators

14. 253 feet

15. (10000, 10000)

16. h = 1.43d + 0.14

17. Because it is so close to the y-intercept. The y-intercept is large based on a large sample size (several hundred days) and the 30 extra pancakes throws off the small input values.

18. R² is the correlation coefficient. Luke’s grades do not follow a logical pattern; they cannot be easily correlated to a linear equation. However, Nick’s grades are steadily improving along a linear equation, this is why his graph has a higher R² (coloration coefficient) value.

19. The equation y = x² is not a linear equation, so the linear line of best fit will not match as well as a quadratic line of best fit would match y = x².

20. 19.23 years

21. (5, 6)

22. A linear model cannot take into account doubling, a better equation would be y = 2^x.

24. M = -3h + 305

25. 7, 19, 27