Chapter 4.4, Problem 16E

a.

To determine

To write:An equation that models the total earnings of the food server as an function of the number of hours.

Answer to Problem 16E

The correct equation is $y=\frac{113}{6}x$ .

Explanation of Solution

Given Information:A table showing the server’s earnings $y$ and $x$ hours.

Graph &Calculation:

Let us make a scatter plot of the given data.

  

Since the scatter plot shows a positive correlation, a line can be fitted to the data.

Using slope-intercept form to write equation utilizing two points $(0,0)$ and $(6,113)$ ,

  $y=mx+b$

  $m=\frac{y_2-y_1}{x_2-x_1}$

  $\begin{array}{l}m=\frac{113-0}{6-0}\\ m=\frac{113}{6}\end{array}$

  $y-\mathrm{int}ercept(b)=0$ $($ when $x=0$ $)$

  $y=\frac{113}{6}x$

Thus, the equation is $y=\frac{113}{6}x$ .

b.

To determine

To interpret:The slope and $y-\mathrm{int}ercept$ of the line of fit.

Answer to Problem 16E

The slope is positive and $y-\mathrm{intercept}$ is $0$ .

Explanation of Solution

Given Information:A table showing the server’s earnings $y$ and $x$ hours.

Interpretation:

The slope of the graph shows the rate of change in earning which is increasing at a rate of $\frac{113}{6}(i.e\mathrm{.18.8})$ .

The $y-\mathrm{intercept}$ represents the earnings when there are no hours spent doing work which is $0$ .