The scatterplot above shows the number of registered voters, x, and the number of people who voted in the last election, y, for seven districts in a town. A line of best fit for the data is also shown. Which of the following could be the equation of the line of best fit?

Options

A. y = −0.5x
B. y = 0.5x
C. y = −2x
D. y = 2x

Answer

B

Explanation

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the graph of the equation and b is the y-coordinate of the y-intercept of the graph. Any two ordered pairs `(x_1, y_1)` and `(x_2, y_2)` that satisfy a linear equation can be used to compute the slope of the graph of the equation using the formula `m=(y_2-y_1)/(x_2-x_1)`. Substituting the coordinates of (120, 60) and (160, 80), which lie on the line of best fit, into this formula gives `m=(80-60)/(160-120)`, which simplifies to `20/40` , or 0.5 . Substituting this value for m in the slope-intercept form of the equation produces y = 0.5x + b. Substituting values from the ordered pair (120, 60) into this equation produces 60 = 0.5(120) + b, so b = 0. Substituting this value for b in the slope-intercept form of the equation produces y = 0.5x + 0, or y = 0.5x.
Choices A, C, and D are incorrect and may result from an error in calculation when determining the slope of the line of best fit.