SATProblem Solving Data Analysis

Scatterplots and Line of Best Fit — SAT Math Guide

Scatterplots and line of best fit SAT questions test your ability to interpret data relationships and make predictions. These problems show you a graph with scattered data points and ask you to analyze trends or use the line of best fit to estimate values. This topic appears frequently in the Problem Solving and Data Analysis domain, with 2-3 questions per SAT math section. You'll master these concepts quickly with the right approach and practice.

What You Need to Know

  • Scatterplot: A graph showing the relationship between two variables using plotted points
  • Line of best fit: A straight line that best represents the trend in scattered data points
  • Positive correlation: As one variable increases, the other increases (upward trend)
  • Negative correlation: As one variable increases, the other decreases (downward trend)
  • No correlation: No clear relationship between the variables (random scatter)
  • Interpolation: Using the line to estimate values within the data range
  • Extrapolation: Using the line to predict values outside the data range
  • Outlier: A data point that falls far from the general trend
  • 📐 KEY FORMULA: Line equation y = mx + b (where m = slope, b = y-intercept)
    💡 PRO TIP: The line of best fit doesn't need to pass through every point — it shows the overall trend.

    How to Solve Scatterplots and Line of Best Fit SAT Questions

    Example Question 1 — Medium Difficulty

    A scatterplot shows the relationship between hours studied and test scores for 20 students. The line of best fit has the equation y = 3.2x + 45. Based on this model, what is the predicted test score for a student who studies 8 hours?

    A) 53
    B) 67.6
    C) 70.4
    D) 74.2
    Solution:
    Step 1: Identify the given equation: y = 3.2x + 45
    Step 2: Substitute x = 8 hours into the equation
    Step 3: Calculate: y = 3.2(8) + 45 = 25.6 + 45 = 70.4
    Answer: C — Substitute the hours studied into the line of best fit equation.

    Example Question 2 — Hard Difficulty

    A scatterplot displays the relationship between the age of a car (in years) and its value (in thousands of dollars). The line of best fit passes through points (2, 18) and (8, 12). If this trend continues, what would be the predicted value of a 12-year-old car?

    A) $6,000
    B) $7,000
    C) $8,000
    D) $9,000
    Solution:
    Step 1: Find the slope using the two points: m = (12 - 18)/(8 - 2) = -6/6 = -1
    Step 2: Use point-slope form with (2, 18): y - 18 = -1(x - 2), so y = -x + 20
    Step 3: Substitute x = 12: y = -12 + 20 = 8
    Answer: C — The predicted value is $8,000 (8 thousand dollars).

    Common SAT Math Mistakes to Avoid

    Mistake: Expecting the line of best fit to pass through all data points
    Fix: Remember the line shows the general trend, not exact values for every point
    Mistake: Confusing correlation with causation
    Fix: The SAT tests correlation (relationship), not whether one variable causes the other
    Mistake: Misreading the scale or units on the axes
    Fix: Always check what each axis represents and the scale increments
    Mistake: Forgetting to convert units in the final answer
    Fix: Pay attention to whether the answer should be in dollars, thousands, percentages, etc.

    Practice Question — Try It Yourself

    A scatterplot shows the relationship between daily temperature (°F) and ice cream sales (in dollars). The line of best fit has equation y = 4.5x - 200. According to this model, what are the predicted ice cream sales when the temperature is 75°F?

    A) $137.50
    B) $200.00
    C) $237.50
    D) $337.50
    Show Answer Answer: A — Substitute x = 75 into y = 4.5x - 200 to get y = 4.5(75) - 200 = 337.5 - 200 = $137.50

    Key Takeaways for the SAT

  • Always identify whether you're looking at a positive, negative, or no correlation
  • Use the line of best fit equation to make predictions by substituting the given x-value
  • Check that your answer makes sense in the context of the problem
  • Watch for outliers that don't follow the general trend
  • Remember that SAT math scatterplots and line of best fit questions often involve real-world scenarios like sales, scores, or measurements
  • Related SAT Math Topics

    Strengthen your SAT math prep with these related topics:

  • Data interpretation →
  • Linear regression correlation →
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