5. a. The slope is (28.75 - 17.60) / (2005 - 1997) = 11.15 / 8 = 1.39375. Using point-slope form with (1997, 17.60): y - 17.60 = 1.39375(x - 1997). Simplifying: y = 1.39375x - 2780.40625 + 17.60 → y = 1.39375x - 2762.80625.
b. For 2009: y = 1.39375 * 2009 - 2762.80625 = 2800.04375 - 2762.80625 = 37.2375. Rounded to nearest cent: $37.24. This is extrapolation since 2009 is outside the data range (1997-2005).
6. a. Plotting points (2001, 2), (2002, 1), (2003, 4), (2004, 6), (2005, 7) shows an upward trend. A line of fit can be drawn.
b. Using points (2001, 2) and (2005, 7): slope = (7 - 2) / (2005 - 2001) = 5 / 4 = 1.25. Point-slope form: y - 2 = 1.25(x - 2001). Simplifying: y = 1.25x - 2501.25 + 2 → y = 1.25x - 2499.25.
7. a. Scatter plot shows a positive linear relationship between average and maximum longevity.
b. Line of fit equation (approximate using visual estimation or calculation): y = 2x + 5 (example; actual may vary based on precise fit).
c. For average longevity x = 33 years: y = 2*33 + 5 = 66 + 5 = 71 years. This is extrapolation if 33 years is beyond the range of the given data points.
Parent Tip: Review the logic above to help your child master the concept of scatter plot and line of best fit worksheet answers.
