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.

Question

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).

Answer 1

To determine which graph shows the line of best fit for the data in Terrence's scatter plot, we need to evaluate the provided options based on how well each line represents the overall trend in a scatter plot characterized by:

• X-values extending from 10 to 90 (practice hours).
• Y-values extending from 0 to 35 (goals scored).

A line of best fit should ideally balance the data points and reflect the general trend without being overly influenced by outliers.

Let's analyze each option:

A: The line passes through (26, 30) and (45, 22). This means that as practice hours increase from 26 to 45, the goals scored appear to decrease, which is counterintuitive. This does not represent a typical trend for practice hours and goals, making it unlikely to be a line of best fit.

B: The line passes through (10, 0), (59, 26), and (70, 32). This shows an increasing trend, as goals scored increase with hours of practice. The inclusion of the point (10, 0) suggests that at minimal practice, no goals are scored, aligning with a reasonable expectation. This looks like a strong candidate for a line of best fit.

C: The line passes through (55, 26) and (59, 26), indicating no change in goals scored (y-value) while the x-value changes. This horizontal line does not reflect an upward or downward trend in practice leading to results, thus it does not serve as a line of best fit.

D: The line passes through (25, 16) and (55, 26). This indicates an increase in goals scored as practice hours increase, similar to option B. However, it does not start from lower values or include a broader spread of data points compared to B, which might make it less representative of the entire dataset.

Based on this analysis, Option B is the most suitable line of best fit because it reflects a consistent increasing trend in the scatter plot, starting from a point that indicates no goals scored with minimal practice and showing growth as more hours are put into practice.

Answer 2

you sure?

Answer 3

Let's carefully consider the options again in detail to ensure we're determining the correct line of best fit for Terrence's dataset based on the information given.

Given Data

• X-values (hours of practice): Range from 10 to 90
• Y-values (goals scored): Range from 0 to 35

A line of best fit should represent the general trend of these data points, ideally showing a positive correlation between practice hours and goals scored.

Analyzing the Options

A:

• Line passes through (26, 30) and (45, 22): This suggests a negative slope (decrease in goals scored as practice hours increase), which is contrary to the typical expectation that more practice leads to more goals. This makes it a poor candidate for a line of best fit.

B:

• Line passes through (10, 0), (59, 26), and (70, 32): This shows a clear positive trend, indicating that as practice hours increase, goals scored also increase. This line is aligned with what we generally expect in sports: more practice results in more goals. This is a strong candidate.

C:

• Line passes through (55, 26) and (59, 26): This is a horizontal line, indicating no change in goals scored with increasing practice hours over this small range (55 to 59). This line does not indicate any trend and thus is not suitable.

D:

• Line passes through (25, 16) and (55, 26): This also shows a positive slope, indicating that goals scored increase with more practice hours. However, without context of a broader range of practice hours and goals, it might not represent the overall trend as effectively as option B, which includes a point at (10, 0) showing lower goals with minimal practice.

Conclusion

After reviewing the options:

• Options A and C are not suitable because they do not align with expected trends.
• Both Options B and D indicate positive correlations, but:
  • B demonstrates a more comprehensive trend starting from (10, 0) and covering a larger range of data.

Thus, based on a closer inspection, Option B remains the most appropriate choice for the line of best fit, as it effectively shows the trend of increasing goals with increasing hours of practice, capturing both lower and higher ranges of practice hours and scores.

If there's any additional specific context you have or if you have the actual scatter plot available for review, feel free to share!