To determine which graph shows the line of best fit for Terrence's scatter plot, we need to consider the nature of best fit lines, which typically represent the overall trend of the data points (i.e., as one variable increases, the other variable tends to increase or decrease).
In this case:
- The x-values (hours at practice) range from 10 to 90.
- The y-values (goals scored) range from 0 to 35.
Let's analyze each option provided:
A. The line passes through (26, 30) and (45, 22). This line suggests that as the hours at practice increase (from 26 to 45), the goals scored decrease (from 30 to 22), which likely does not represent a positive correlation typically expected in a sports context. So this is not a good fit.
B. The line passes through (10, 0), (59, 26), and (70, 32). This line starts at the origin and shows a positive trend, where more hours of practice relate to more goals scored, indicative of a potential positive correlation.
C. The line passes through the points (55, 26) and (59, 26). This line is horizontal (no change in the y-value as the x-value changes), which suggests that players who practice for 55 to 59 hours all scored 26 goals. This flat line does not adequately represent a trend in a scatter plot typically, either.
D. The line passes through (25, 16) and (55, 26). This line also shows an upward trend, where increased practice hours from 25 to 55 correlate positively with goals scored, which also indicates a good fit.
From this analysis, both B and D show positive correlations. However, B has clearer points showcasing an upward trend starting from near the origin (10, 0).
Conclusion: The best choice for the line of best fit based on described characteristics of the data points is:
B.