Question the-st

3.4 Two-Variable Data & Models - Line of best fit
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The sterplot shows the relationship between two variables, x and y . A line of best fit is also shown.

  • The sterplot 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.
    • 2 points are touching the line of best fit.
    • 3 points are above the line of best fit.
    • 5 points are below the line of best fit.
    • The line of best fit passes through the following approximate coordinates:
      • (0 comma 12.9)
      • (6 comma 8)
      • (12 comma 3.2)

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

A.

-2.4

B.

-0.8

C.

0.8

D.

2.4

The sterplot shows the relationship between two variables, x and y . A line of best

Hard-difficulty · SAT Math · Two-Variable Data & Models — Line of best fit. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

Choice B is correct. A line of best fit is shown in the sterplot such that as the value of x increases, the value of y decreases. Thus, the slope of the line of best fit shown is negative. The slope of a line passing through two points, x1,y1 and x2,y2, can be calculated as y2-y1x2-x1. The line of best fit shown passes approximately through the points 1,12 and 11,4. Substituting 1,12 and 11,4 for x1,y1 and x2,y2, respectively, in y2-y1x2-x1 gives 4-1211-1, which is equivalent to -810, or -0.8. Therefore, of the given choices, -0.8 is closest to the slope of the line of best fit shown.

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

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

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