Problem-Solving and Data AnalysisHardLine matching a falling scatterplot
Problem-Solving and Data Analysis practice question
A scatterplot shows the points (1, 10), (2, 8), (3, 6) and (4, 4). Which equation best represents the line of best fit for these points?
- A. y = −2x + 12Correct
- B. y = 2x + 12
- C. y = −2x + 10
- D. y = −x + 11
Answer: A. y = −2x + 12
y falls by 2 for each 1-unit rise in x, so the slope is −2. At x = 1, y = 10 = −2(1) + 12, so the intercept is 12. All four points lie exactly on y = −2x + 12.
Why the other answers are wrong
- B. y = 2x + 12
- A positive slope would have y rising with x; the points fall.
- C. y = −2x + 10
- −2x + 10 gives 8 at x = 1, but the point there is (1, 10).
- D. y = −x + 11
- −x + 11 gives 10 at x = 1 but 9 at x = 2, not 8; the drop per step is 2, not 1.
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