Math Problem Statement
Solution
The image shows two scatter plots, each representing "Hours of Practice per Week" on the x-axis and "Number of Games Won" on the y-axis. There are two lines of best fit drawn in each plot, and the question asks which line was drawn correctly to make predictions. Additionally, it asks what the best prediction of the number of games won is if the team practiced 3 hours per week.
- The purple line on the left seems to have a higher slope, predicting a steeper increase in games won with practice.
- The orange line on the right has a lower slope, making a more moderate prediction.
To answer the question:
- For 3 hours of practice per week:
- On the purple line (Justin’s line), it crosses approximately at 15 games.
- On the orange line (Brian’s line), it crosses around 12 games.
Given that the orange line (Brian’s) fits the data points better, Brian’s line of best fit is more accurate. The correct prediction based on Brian's line for 3 hours of practice is 12 games.
Therefore, the correct answer is B. Brian; 12 games.
Would you like more details on how to draw lines of best fit or explore related concepts?
5 Follow-Up Questions:
- How do you determine the line of best fit for a set of data?
- What does the slope of the line of best fit represent in this context?
- How would increasing practice time beyond 5 hours affect the prediction?
- Could the accuracy of the prediction change if we had more data points?
- How can residuals be used to check the fit of a line?
Tip:
When drawing a line of best fit, ensure that the line passes as close as possible to all data points, balancing the distance above and below the line for an accurate prediction.
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Math Problem Analysis
Mathematical Concepts
Scatter plots
Lines of best fit
Slope
Formulas
y = mx + b (Equation of a line)
Slope formula (change in y over change in x)
Theorems
Line of best fit
Suitable Grade Level
Grades 7-10
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