Problem-Solving and Data Analysis · Math
Two-variable data and models
Scatterplots and lines of best fit: interpreting slope and intercept, and comparing an actual value to a predicted one.
12 questions in the bank · 2 easier · 6 medium · 4 harder · this domain is ≈15% of the section
What to watch for
A line of best fit predicts a trend; individual points are not required to sit on it. 'Above the line' means actual minus predicted is positive, not that the value is large.
How the question is worded
These are the actual stems used in the bank — the SAT reuses a small set of wordings, and recognising them saves time on test day.
- A scatterplot relates x, the hours a student practiced typing, to y, the typing speed in words per minute. The line of best fit has equation y = 5x + 40. What y-value does the line predict when x = 11?
- A scatterplot relates x, the weeks after planting, to y, the height of a sunflower in centimeters. The line of best fit has equation y = 2x + 30. What y-value does the line predict when x = 10?
- A scatterplot relates x, the outdoor temperature in °C, to y, the cups of hot cocoa a café sold. The line of best fit has equation y = 6x + 30. What y-value does the line predict when x = 9?
- A scatterplot relates x, the years since a trail opened, to y, the annual visitors in thousands. The line of best fit has equation y = 2x + 10. What y-value does the line predict when x = 9?
Worked examples
easyA scatterplot relates x, the hours a student practiced typing, to y, the typin…
A scatterplot relates x, the hours a student practiced typing, to y, the typing speed in words per minute. The line of best fit has equation y = 5x + 40. What y-value does the line predict when x = 11?
Answer: 95
Explanation
Substitute x = 11 into the fit: y = 5·11 + 40 = 95. A line of best fit is a prediction tool — plugging in is all this asks.
mediumA scatterplot relates x, the outdoor temperature in °C, to y, the cups of hot …
A scatterplot relates x, the outdoor temperature in °C, to y, the cups of hot cocoa a café sold. The line of best fit has equation y = 6x + 30. What y-value does the line predict when x = 9?
Answer: 84
Explanation
Substitute x = 9 into the fit: y = 6·9 + 30 = 84. A line of best fit is a prediction tool — plugging in is all this asks.
hardThe table shows four (x, y) data points. The line of best fit for the data has…
The table shows four (x, y) data points. The line of best fit for the data has equation y = 4x + 5. For which value of x is the actual y-value the greatest amount ABOVE the value predicted by the line?
- A. x = 8
- B. x = 5
- C. x = 1
- D. x = 9
Answer: C. x = 1
Explanation
Compute predicted values 4x + 5 for each x and subtract: the gaps are +7, −3, −6, +4 at x = 1, 5, 8, 9 respectively. The largest positive gap (+7) is at x = 1. “Above the line” means actual minus predicted is positive — not merely a large y.