Interpreting the Line of Best Fit
The line of best fit summarizes a scatterplot's trend and lets you predict — within the data's range.
Reading the concept isn't enough. The score comes from practicing the real Bluebook-style format and finding the exact mistakes you keep making.
What the SAT tests here
Plug the given value into the line's equation to predict. Read carefully whether you're given $x$ and asked for $y$ or the reverse. Predictions far outside the data range (extrapolation) are unreliable.
How to solve one, step by step
Example: the fit is $y = 2x + 5$. Predict $y$ at $x = 10$.
- Substitute: $2(10) + 5$.
- Predicted $y = 25$.
The mistakes that cost points
- Reading the line at the wrong variable. If asked for $y$, substitute the given $x$ — not the reverse.
- Extrapolating without caution. Predicting well beyond the data range isn't supported by the line.
Practice questions
Try these the way you would on test day, then open the solution to check your method.
Easy
The scatterplot shows the relationship between hours studied and test score for 8 students. A line of best fit is also shown. Based on the line of best fit, what is the predicted test score for a student who studies for 4 hours?
- A56
- B70
- C68
- D62
Show solution
Answer: D, 62. The line of best fit passes through $(0, 50)$ and $(10, 80)$, so its slope is $\frac{80 - 50}{10 - 0} = 3$ points per hour. At $x = 4$: predicted score $= 50 + 3(4) = 62$.
Medium
The line of best fit for a dataset is $y = -3x + 90$, where $x$ is months since a product launched and $y$ is weekly sales (in thousands). A student wants to find the month when weekly sales are predicted to reach 60 thousand. What is that month?
- A$x = 10$
- B$x = 60$
- C$x = -3$
- D$x = 30$
Show solution
Answer: A, $x = 10$. Set $y = 60$: $60 = -3x + 90 \Rightarrow -30 = -3x \Rightarrow x = 10$.
Hard
The scatterplot shows items produced per hour and defect rate (%) in a manufacturing plant. A line of best fit is shown. A quality manager claims that at 90 items per hour the defect rate will be 0%. Based on the line of best fit, what does the model actually predict at 90 items per hour?
- AApproximately 2% — the manager's claim is not supported
- BApproximately 3% — the line continues its current slope
- CThe defect rate cannot be predicted beyond 80 items per hour
- D0% — the line reaches zero at 90 items per hour
Show solution
Answer: A, Approximately 2% — the manager's claim is not supported. The line passes through $(30, 8)$ and $(80, 3)$, giving slope $= \frac{3 - 8}{80 - 30} = -0.1$. The equation is $y = -0.1x + 11$. At $x = 90$: $y = -0.1(90) + 11 = 2\%$. The claim of $0\%$ is not supported.
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