Math Problem Statement

Which graph shows a properly drawn line of best fit?

Solution

The question is asking which of the four graphs shows a properly drawn line of best fit.

  1. Graph (1): The line appears curved and does not pass through the data points in a consistent pattern.
  2. Graph (2): The line is straight but does not fit the overall trend of the data points well. It doesn't balance the points above and below the line.
  3. Graph (3): The line is a good fit for the data points. It is straight and evenly balances the data points above and below it.
  4. Graph (4): The line is curved, similar to graph (1), which may not be the best fit for the points shown.

Therefore, Graph (3) is the correct answer, as it properly shows a line of best fit that balances the data points evenly and follows the trend.

Would you like further clarification on how a line of best fit works?

Here are 5 related questions you might find useful:

  1. What are the criteria for determining a good line of best fit?
  2. How do you calculate a line of best fit mathematically?
  3. Why is a curved line sometimes used instead of a straight line for best fit?
  4. Can there be multiple lines of best fit for a given data set?
  5. How does the method of least squares work in finding the line of best fit?

Tip: The line of best fit minimizes the sum of the squares of the vertical distances between the data points and the line. This is why it often represents the overall trend accurately.

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Math Problem Analysis

Mathematical Concepts

Statistics
Line of Best Fit
Trend Line

Formulas

y = mx + b (equation of a straight line)
Least Squares Method

Theorems

Least Squares Theorem

Suitable Grade Level

Grades 8-10