1. Negative correlation. As the number of students trained (x) increases, the number of calls (y) decreases, indicating a negative relationship.
2. The scatter plot should show the population (in thousands) on the y-axis and the year on the x-axis. Plot the points: (1970, 50), (1980, 35), (1990, 45), (2000, 30), (2001, 60), (2002, 65), (2003, 70).
3. Draw a line that best fits the data points on the scatter plot, minimizing the distance from the points to the line.
4. The graph shows a positive correlation. As time increases, the distance traveled increases.
5. The slope is calculated as (change in y) / (change in x). For points (25, 2001) and (60, 2003), the slope is (2003 - 2001) / (60 - 25) = 2 / 35 ≈ 0.0571.
6. Using point-slope form: y - y1 = m(x - x1). Using point (25, 2001) and slope 2/35: y - 2001 = (2/35)(x - 25). Simplifying, y = (2/35)x + 2001 - (50/35) = (2/35)x + 1997.57.
7. Using the equation y = (2/35)x + 1997.57, substitute x = 70: y = (2/35)(70) + 1997.57 = 4 + 1997.57 = 2001.57. The predicted population in 2003 is 2001.57 thousand, or approximately 2002 thousand.
8. The graph shows a positive correlation.
9. From the graph, at time = 4, the distance travelled is approximately 50.
10. From the graph, at time = 2, the distance travelled is approximately 30.
Parent Tip: Review the logic above to help your child master the concept of scatter plot and lines of best fit worksheet.
