Exploring bivariate data Student Activity Sheet 4; use with Exploring Interpreting linear models

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Nickolas O’Connor’
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1 1. What is Hooke s Law? 2. What item in the science experiment is being used to simulate a spring? 3. Fill in the table (for number of marbles = {0, 5, 10, 15}) with the data collected during the science experiment. Number of marbles 0 [1] Distance (cm) from table to top of cub [2] Distance (cm) from table to bottom or cup [3] Distance (cm) from bottom of cup to floor Fill in the table in question 3 (for number of marbles = {20, 25, 30}) with the rest of the data from the experiment. Page 1 of 8

2 5. Make a scatterplot to show the data for the number of marbles and the distance from the table to the top of the cup (Distance [1]). Does your scatterplot indicate a positive, negative, or no correlation between the number of marbles and distance from the table? Explain. 6. Find the change in the distance (cm) from the table to the top of the cup, (Distance 1), each time 5 marbles are added. Stretch-It Experiment Distance 1: from Number of table to top of cup marbles in centimeters Page 2 of 8

3 7. Based on your analysis of the data, is a linear model appropriate? Why or why not? 8. What is the initial distance of the cup from the table (when marbles = 0)? 9. What number could approximate the slope of a trend line for these data? 10. Use the information in questions 8 and 9 to write the function rule for a trend line for these data. Page 3 of 8

4 Use the information in the table about the number of marbles and the distance from the table to the bottom of the cup (Distance 2) to complete statements Use the answer choices provided The average difference in the distance is cm. 12. The average rate of change per marble is cm/marble. 13. The y-intercept is. This point represents the distance from the table to the bottom of the cup when there are marbles in the cup. 14. An equation for a trend line modeling these data could be y = x +. Page 4 of 8

Use the information in the table about the number of marbles and the distance from the bottom of the cup to the floor (Distance 3) to complete statements 15 18. Use the answer choices provided. 0 0.

5 Use the information in the table about the number of marbles and the distance from the bottom of the cup to the floor (Distance 3) to complete statements Use the answer choices provided The average difference in the distance is cm. 16. The average rate of change per marble is cm/marble. 17. The y-intercept is. This point represents the distance from the bottom of the cup to the floor when there are marbles in the cup. 18. An equation for a trend line modeling these data could be y = x +. Use the following graph, which displays the trend lines for Distance 1, Distance 2, and Distance 3, to complete statements 19 and 20. Use the answer choices provided. negative increasing positive table decreasing rubber band cup 19. The slopes for the bottom two trend lines are, because these distances are. The slope for the third trend line is, because its distance is. 20. The difference between the y-intercepts of the trend lines for Distances 1 and 2 represents the length of the in the experiment. Page 5 of 8

Use your trend lines or the patterns in the data in the following table to complete statements 21 23. Use the answer choices provided. 19.108 48.64 cups 22.136 35 number of marbles centimeters 21.

6 Use your trend lines or the patterns in the data in the following table to complete statements Use the answer choices provided cups number of marbles centimeters 21. With 42 marbles, the top of the cup would be cm from the table. 22. When the cup s bottom is cm from the floor, the cup will have marbles. With at least 40 marbles, the cup s bottom is at least cm from the floor. 23. The units for the slope in the trend lines are per. Page 6 of 8

24. REINFORCE Four cars started from the same city at the same time. The following data were collected on the performance of the four cars, based on miles driven in terms of hours.

7 24. REINFORCE Four cars started from the same city at the same time. The following data were collected on the performance of the four cars, based on miles driven in terms of hours. Use these tables to answer parts a-f below. Car A Car B Car C Car D Hours Miles Hours Miles Hours Miles Hours Miles a. Which car was traveling the fastest? How do you know? b. Which car was traveling the slowest? How do you know? c. Compare and contrast the tables. Page 7 of 8

8 d. Write a function rule to model each car s travel. Car A Car B Car C Car D e. On a single graph, create a scatterplot for each table. Compare and contrast the graphs. f. Do any of the tables represent a proportional relationship? Explain how you know. Page 8 of 8

y-intercept remains constant?

1. The graph of a line that contains the points ( 1, 5) and (4, 5) is shown below. Which best represents this line if the slope is doubled and the y-intercept remains constant? F) G) H) J) 2. The graph