Chapter 4.1, Problem 36E

a.

To determine

To estimate: The slope and $y-\mathrm{intercept}$ of the graph.

Answer to Problem 36E

  $\mathrm{Slope}=0.2$ and $y-\mathrm{intercept}(b)=8$ .

Explanation of Solution

Given Information: A graph is given.

Calculation:

Examining the given graph, it can be observed that two points are,

  $(0,8)$ and $(10,10)$ .

  $m=\frac{y_2-y_1}{x_2-x_1}$

Substituting the given values to find $m$ ,

  $\begin{array}{l}m=\frac{10-8}{10-0}\\ m=\frac{2}{10}\\ m=0.2\end{array}$

  $y-\mathrm{intercept}(b)=8$ $($ when $x=0$ $)$

Thus, m is $0.2$ and $y-\mathrm{intercept}$ is $8$ .

b.

To determine

To interpret: Slope and $y-\mathrm{intercept}$ in context of the problem.

Explanation of Solution

Given information: $m=0.2$ and $y-\mathrm{intercept}(b)=8$ .

Interpretation:

  $m=0.2$ , this implies that slope is positive, and the box office revenues keep on increasing year on year.

  $y-\mathrm{intercept}(b)=8$ , this means that in year $2000$ the revenue was $8$ billion.

Thus, required interpretations are done.

c.

To determine

The way to predict the future box office revenue.

Answer to Problem 36E

Box office revenue in year $2018$ will be $\$11.6$ billion.

Explanation of Solution

Given Information: $m=0.2$ and $y-\mathrm{intercept}(b)=8$ (from part $a$ ), the data to be predicted should be of year $2018$ .

Calculation:

Slope intercept form: $y=mx+b$

Substituting the values,

  $y=0.2x+8$

As is given $x=18$ , so

  $\begin{array}{l}y=0.2x+8\\ y=0.2(18)+8\\ y=3.6+8\\ y=11.6\end{array}$

Thus, box office revenue in year $2018$ will be $\$11.6$ billion.