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Test
Math
Domain
Problem-Solving and Data Analysis
Skill
Two-variable data: Models and scatterplots
Difficulty
Easy
ID: 39aa146d
Modded SAT Question Bank by Abdullah Mallik

The scatterplot shows the relationship between x and y. A line of best fit is also shown.

  • The scatterplot has 6 data points.
  • The data points are in a linear pattern trending up from left to right.
  • A line of best fit is shown:
    • The line of best fit slants up from left to right.
    • 1 point is touching the line of best fit.
    • 2 points are above the line of best fit.
    • 3 points are below the lines of best fit.
    • The line of best fit passes through the following approximate coordinates:
      • (0 comma 0.2)
      • (4 comma 2)

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

  1. -2.27

  2. -0.44

  3. 0.44

  4. 2.27


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Correct Answer: C
Rationale

Choice C is correct. It's given that the scatterplot shows the relationship between two variables, x and y, and a line of best fit is shown. For the line of best fit shown, for each increase in the value of x by 1, the corresponding value of y increases by a constant rate. It follows that the relationship between the variables x and y has a positive linear trend. A line in the xy-plane that passes through the points a,b and c,d has a slope of d-bc-a. The line of best fit shown passes approximately through the points 0,0.25 and 4,2. It follows that the slope of this line is approximately 2-0.254-0, which is equivalent to 0.4375. Therefore, of the given choices, 0.44 is closest to the slope of the line of best fit shown.

Choice A is incorrect. This is the slope of a line of best fit for a relationship between x and y that has a negative, rather than a positive, linear trend.

Choice B is incorrect. This is the slope of a line of best fit for a relationship between x and y that has a negative, rather than a positive, linear trend.

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

Question Difficulty: Easy
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