Chapter 4.4, Problem 9PPS

(a)

To determine

To write: the slope intercepts form of an equation for the line of fit shown in the scatter plot.

Answer to Problem 9PPS

The equation in slope intercept form for the line of it.

  $y=224.25x+68837.5$

Explanation of Solution

Given information:

Use the scatter plot.

Use the points $\left(6,70,183\right)$ and $\left(10,71,1080\right)$ .

  

Calculation:

Find the slope of the line containing the given points,

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{71080-70183}{10-6}\\ m=\frac{897}{4}\\ m=224.25\end{array}$

Use the slope and either of the two points, to find the $y$ intercept.

  $\begin{array}{c}y=mx+b\\ 71080=224.25\left(10\right)+b\\ b=71080-2242.5\\ =68837.5\end{array}$

Now, write the equation in slope intercept form for the line of it.

  $\begin{array}{l}y=mx+b\\ y=224.25x+68837.5\end{array}$

(b)

To determine

To predict: the average attendance at a game in 2025.

Answer to Problem 9PPS

The average attendance at Buffalo Bills game in 2020 will be 73323 people

Explanation of Solution

Given information:

Use the scatter plot.

Use the points $\left(6,70,183\right)$ and $\left(10,71,1080\right)$ .

  

Calculation:

Substitute 20for $x$ in the equation from part (a).

Now, solve the equation as shown,

  $\begin{array}{l}y=224.25x+68837.5\\ y=224.25\left(20\right)+68837.5\\ y=4485+68837.5\\ y=73322.5\end{array}$

The average attendance at Buffalo Bills game in 2020 will be 73323 people.

(c)

To determine

Whether the equation can be used to make a decision about the average attendance in any given year in the future.

Answer to Problem 9PPS

No.

Explanation of Solution

Given information:

Use the scatter plot.

Use the points $\left(6,70,183\right)$ and $\left(10,71,1080\right)$ .

  

Calculation:

No, can’t use this equation to make predictions about future attendance because the average attendance will fluctuate with other variable such as how good the team is that year.