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Test
Math
Domain
Problem-Solving and Data Analysis
Skill
Two-variable data: Models and scatterplots
Difficulty
Medium
ID: 2e74e403
Modded SAT Question Bank by Abdullah Mallik

In the given scatterplot, a line of best fit for the data is shown.

  • The scatterplot has 10 data points.
  • The data points are in a linear pattern trending down from left to right.
  • A line of best fit is shown:
  • The line of best fit slants down from left to right.
    • 5 points are touching the line of best fit.
    • 2 points are above the line of best fit.
    • 3 points are below the line of best fit.
    • The line of best fit passes through the following approximate coordinates:
      • (1 comma 7)
      • (4 comma 5)
      • (10 comma 1)

Which of the following is closest to the slope of this line of best fit?

  1. 7

  2. 0.7

  3. -0.7

  4. -7


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Correct Answer: C
Rationale

Choice C is correct. A line of best fit is shown in the scatterplot such that as the value of x increases, the value of y decreases. It follows that the slope of the line of best fit shown is negative. The slope of a line in the xy-plane that passes through the points x1,y1 and x2,y2 can be calculated as y2-y1x2-x1. The line of best fit shown passes approximately through the points 0,8 and 10,1. Substituting 0,8 for x1,y1 and 10,1 for x2,y2 in y2-y1x2-x1 yields the slope of the line being approximately 1-810-0, which is equivalent to -710, or -0.7. Therefore, of the given choices, -0.7 is the closest to the slope of this line of best fit.

Choice A is incorrect. The line of best fit shown has a negative slope, not a positive slope.

Choice B is incorrect. The line of best fit shown has a negative slope, not a positive slope.

Choice D is incorrect and may result from conceptual or calculation errors.

Question Difficulty: Medium
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