Question

the scatter plot shows the price, in cents, of a postage stamp used to mail a letter in the united states for the years from 1958 to 2014. also shown is a line of fit to model the data. postage stamp price the equation of the line of fit is ( y = - 0.71 + 0.86x ), where ( y ) represents the predicted price, in cents, of a stamp and ( x ) represents the number of years since 1958. which statement best describes the model? a. the model estimates an increase, on average, of 0.71 cent per year in the price of a stamp. b. the model estimates a decrease, on average, of 0.71 cent per year in the price of a stamp. c. the model estimates an increase, on average, of 0.86 cent per year in the price of a stamp. d. the model estimates a decrease, on average, of 0.86 cent per year in the price of a stamp.

Explanation:

Step1: Recall the slope - intercept form of a linear equation

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. In the given equation \(y=-0.71 + 0.86x\), \(m = 0.86\) and \(b=-0.71\).

Step2: Interpret the slope

The slope \(m\) represents the rate of change. Since \(x\) represents the number of years since 1958 and \(y\) represents the price of a stamp in cents, a positive slope \(m = 0.86\) means that for each additional year (\(\Delta x=1\)), the value of \(y\) (price of the stamp) changes as \(\Delta y=m\Delta x\). When \(\Delta x = 1\), \(\Delta y=0.86\times1 = 0.86\). A positive slope indicates an increase.

Answer:

C. The model estimates an increase, on average, of 0.86 cent per year in the price of a stamp.