The scatterplot in the standard (x, y) coordinate plane below contains data points

The scatterplot in the standard (x, y) coordinate plane below contains data points showing a strong linear correlation between the variables x and y. Mia drew the line shown to model the data. One of the following equations represents Mia’s line. Which one?

  1. y = -3x + 8
  2. y = -3x + 10
  3. y = -2x + 10
  4. y = 2x + 10
  5. y = 2x + 8

Answer

The correct answer is B.

The line on the graph has a negative linear correlation because as x increases y decreases. The line goes through the points (0, 10) and (3, 1).

To find the slope, m = (y1 - y2)/(x1 - x2)

m = (10 - 1)/(0 - 3) = -3

The y-intercept, where the line crosses the y-axis, is at +10. Insert m and y into slope-intercept form of the equation, y = mx + c.

y = -3x + 10