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Terrence created a scatter plot to represent the total number of goals scored by each player on his soccer team in a season and the number of hours the player spent at soccer practice.

The scatter plot has 10 data points. The x-values of the data points extend from 10 to 90, and the y-values of the data points extend from 0 to 35.

Which graph shows the line of best fit for the data in Terrence's scatter plot?
A.
The scatter plot has 10 data points. The x-values of the data points extend from 10 to 90, and the y-values of the data points extend from 0 to 35. A line is line passing through the points (26, 30) and (45, 22).

B.
The scatter plot has 10 data points. The x-values of the data points extend from 10 to 90, and the y-values of the data points extend from 0 to 35. A line is line passing through the points (10, 0), (59, 26) and (70, 32).

C.
The scatter plot has 10 data points. The x-values of the data points extend from 10 to 90, and the y-values of the data points extend from 0 to 35. A line is line passing through the points (55, 26) and (59, 26).

D.
The scatter plot has 10 data points. The x-values of the data points extend from 10 to 90, and the y-values of the data points extend from 0 to 35. A line is line passing through the points (25, 16) and (55, 26).

1 answer

To determine which graph shows the line of best fit for the data in Terrence's scatter plot, we consider both the direction and trend of the data points:

  • Best Fit Line: A line of best fit captures the overall trend of the data points, indicating the relationship between practice hours (x-values) and goals scored (y-values). It should not necessarily pass through any specific data points but should minimize the distance to all points.

We analyze the options:

  • Option A: The line passes through (26, 30) and (45, 22). This line seems to have a negative slope, which implies that as practice hours increase, the goals decrease. This is unlikely if practice hours generally lead to more goals.

  • Option B: The line passes through (10, 0), (59, 26), and (70, 32). This line has a positive slope, suggesting that more practice hours result in more goals scored, which is typically expected in sports.

  • Option C: The line passes through (55, 26) and (59, 26). This line is horizontal, indicating that no matter the practice hours (within this small range), the goals scored remain constant, which is unlikely as a trend overall.

  • Option D: The line passes through (25, 16) and (55, 26). This line has a positive slope as well, indicating that more practice hours are associated with higher goals scored.

Considering all options, Option B and Option D appear to show positive relationships. However, Option B has a clearer upward trend since it accounts for a wider range of x-values and clearly illustrates that more practice leads to more goals.

Thus, the best line of best fit for Terrence's scatter plot is:

B.