Question

the graph shows information on the average number of americans who viewed the nightly news from 1980 to 2010. a line of best fit is shown on the scatterplot, where t represents years since 1980 and v represents the average number of nightly news viewers, in millions, for that year. according to the model, which of the following is the best interpretation of the slope of this line? choose 1 answer: a from 1980 to 2010, the number of americans who viewed the nightly news decreased by about 1 million viewers. b from 1980 to 2010, the number of americans who viewed the nightly news decreased by about 1 million viewers per year. c from 1980 to 2010, the number of americans who viewed the nightly news decreased by about 0.2 million viewers per year. d from 1980 to 2010, the number of americans who viewed the nightly news decreased by about 2% each year.

Explanation:

The slope of a line in a linear - regression context (line of best fit) represents the rate of change. Here, the x - variable is years since 1980 and the y - variable is the number of nightly news viewers in millions. A negative slope means a decrease in the number of viewers over time. To find the slope, we can estimate two points on the line. For example, at \(t = 0\) (1980), \(V\approx50\) million and at \(t = 25\) (2005), \(V\approx25\) million. The change in \(V\) (\(\Delta V\)) is \(25 - 50=- 25\) million and the change in \(t\) (\(\Delta t\)) is 25 years. The slope \(m=\frac{\Delta V}{\Delta t}=\frac{25 - 50}{25}=-1\) million viewers per year. This means the number of viewers decreased by about 1 million viewers per year.

Answer:

B. From 1980 to 2010, the number of Americans who viewed the nightly news decreased by about 1 million viewers per year.