Name Date Period State Scatter Plots and the U.S. Congress I - The House of Representatives: The following table shows the approximate population for some states along with the number of members each state has in the House of Representatives. This information is based on the 2010 census. Approximate population in millions The number of members in the House of Representatives Arizona 6.4 9 Colorado 5.0 7 Connecticut 3.6 5 Georgia 9.7 14 Idaho 1.6 2 Iowa 3.1 4 Minnesota 5.3 8 New Jersey 8.8 12 Washington 6.8 10 West Virginia 1.9 3 1. Make a scatter plot of the data. y Population and Number of House Members Source : (Page 5 & 6 of) http://fpc.state.gov/documents/organization/155584.pdf Number of members in the House of Representatives x Estimated population (millions) Page 1 of 8
2. Does the scatter plot on the previous page show positive, negative, or no correlation? Please explain your answer. 3. Draw a best fit line through the points on the previous page. Remember, a best fit line is a line on a scatter plot drawn near the points. 4. Use your graphing calculator to find the equation of your best fit line. Please see the PowerPoint presentation to guide you through this part! 5. Write your equation from #4 below. 6. The 1.4 in your equation above represents the slope. What does this number tell you about the rate of change in house members? Please continue to the next page Page 2 of 8
7. According to the 2010 census, Kentucky has a population of about 4.4 million people. a) Use the graph on page 1 to estimate how many House members Kentucky had in 2010. b) Use the equation that you wrote in #5 on the previous page to estimate how many House members Kentucky had in 2010. 8. According to the 2010 census, New York has a population of about 19.4 million people. a) Use the graph on page 1 to approximate the number of house members in New York In 2010. If you are not able to use the graph to answer this question, explain why. b) Use the equation that you wrote in #5 on the previous page to estimate how many House members New York has. 9. According to the 2010 census, California has 53 members in the house of representatives. Use the equation that you wrote in #5 to figure out the approximate population of California in 2010 Do an internet search California s population in 2010 to see how accurate your answer is! 10. According to the 2010 census, there are a total of 435 members in the house of representatives. Use the equation that you wrote in #5 to figure out the approximate population of the United States in 2010. Do an internet search on the population of the U.S. in 2010 to see how accurate your answer is! Page 3 of 8
II - The United States Senate: The following tables looks similar to the table on the top of page 1. It still shows shows the estimated population for some states. However, this time it shows the members each state has in the United States Senate. Again, this information is based on the 2010 census. State 11. Graph the data. Approximate population in millions The number of members in the Senate Arizona 6.4 2 Colorado 5.0 2 Connecticut 3.6 2 Georgia 9.7 2 Idaho 1.6 2 Iowa 3.1 2 Minnesota 5.3 2 New Jersey 8.8 2 Washington 6.8 2 West Virginia 1.9 2 y Population and Number of Senate Members Source : (Page 5 & 6 of) http://fpc.state.gov/documents/organization/155584.pdf Number of members in the Senate x Estimated population (millions) Page 4 of 8
12. Draw a horizontal line through the points on the previous page. 13. Find the slope of the line on the previous page. What does the slope tell you about the rate of change in senate members? 14. Write an equation that describes the relationship between the U.S. population and the number of members in the U.S. Senate. Let x represent the population in millions, and let y represent the number of members in the U.S. senate. Don t over think this question. It is pretty straight-forward, and a formula is not necessary. 15. According to the 2010 U.S. census, Texas has a population of about 25.3 million people. How many senate members does Texas have? 16. According to the 2010 U.S. census, Montana has a population of about 1 million people. How many senate members does Montana have? 17. How many total members are there in the U.S. Senate? Page 5 of 8
III Running Out of Money: The following table shows the relationship between time and the balance in a savings account. Time (months) 1 3 5 8 9 Balance in Savings: Beginning of Month ($) 2296 2103 1827 1500 1407 18. Make a scatter plot of the data. y Balance in savings: beginning of month ($) x Time (months) 19. Does the scatter plot above show positive, negative, or no correlation? Please explain your answer. 20. Draw a line through the points. Page 6 of 8
21. Use your graphing calculator to find the equation of your best fit line. Please see the PowerPoint presentation to guide you through this part! 22. Write your equation from #21 below. 23. The 2,417.24 in your equation above represents the y-intercept. What does this number mean in terms of this problem? 24. The -113.58 in your equation above represents the slope. What does this number tell you about the rate of change for the balance in the savings account. Page 7 of 8
25. a) Use the graph on page 6, to estimate the balance in the savings at the beginning of of 7 months. b) Use the equation that you wrote in #22 on the previous page to estimate the balance in the savings at the beginning of 7 months. Please show your work. 26. a) Use the graph on page 6 to estimate when the balance in the account is $2,000. b) Use the equation that you wrote in #22 on the previous page to estimate when the balance in the account is $2,000? Please show you work. 27. a) Use the graph on page 6 to estimate when there is no money left in the account. If you are not able to use the graph to answer this question, explain why. b) Use the equation that you wrote in #22 on the previous page to estimate when there is no money left in the account. Please show your work. Page 8 of 8