Chapter 8.9, Problem 4PPS

a.

To determine

To find: An equation in slope intercept form for the line of fit.

Answer to Problem 4PPS

  $y=-17x+416$

Explanation of Solution

Given information:

The line of fit drawn shows the number of fan clubs in the U.S. for several years following 1999.

  

Calculation:

The line passes through the point $(4,348)$ and $(6,314)$ .

Then, slope of the line,

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ \Rightarrow m=\frac{314-348}{6-4}[\text{Using }(x_1,y_1)=(4,348),(x_2,y_2)=(6,314)]\\ \Rightarrow m=\frac{-34}{2}\\ \Rightarrow m=-17\end{array}$

The equation of line in point slope form is given by,

  $\begin{array}{l}y-y_1=m(x-x_1)\\ \Rightarrow y-348=-17(x-4)[\text{Replacing }m=-17,(x_1,y_1)=(4,348)]\\ \Rightarrow y-348=-17x+68[\because a(b-c)=ab-ac]\\ \Rightarrow y=-17x+68+348\\ \Rightarrow y=-17x+416\end{array}$

Thus, the equation of the line in slope intercept form is $y=-17x+416$ .

b.

To determine

To calculate: The number of fan clubs in the U.S. in 2012.

Answer to Problem 4PPS

195.

Explanation of Solution

Given information:

The line of fit drawn shows the number of fan clubs in the U.S. for several years following 1999.

  

Calculation:

Number of years between 1999 and 2012 $=2012-1999=13$

The equation of the line of fit is,

  $\begin{array}{l}y=-17x+416\\ \Rightarrow y=-17(13)+416[\text{Replacing }x=13]\\ \Rightarrow y=-221+416\\ \Rightarrow y=195\end{array}$

There should be 195 fan clubs in the U.S. in 2012.