Chapter 6.4, Problem 16PPS

(a)

To determine

To find: Which situation is proportional.

Answer to Problem 16PPS

The graph B is proportional

Explanation of Solution

Given: Suppose Isabel decide to save $\$20$ each week for her family. Her sister already has $\$10$ and wants to save $\$20$ each week.

  

Given:

From the graph given it is concluded that

The graph B is proportional because the rates are consistent.

The graph A does not have the same rate.

(b)

To determine

To Compare: The graphs. Which graph represents the proportional situation.

Answer to Problem 16PPS

The graph B is proportional

Explanation of Solution

Given: Suppose Isabel decide to save $\$20$ each week for her family. Her sister already has $\$10$ and wants to save $\$20$ each week.

  

Given:

From the graph given it is concluded that

The graph B is proportional because the rates are consistent.

The graph A does not have the same rate.

As

In the graph B in the first week the money save is $\$20$ thus making the rate of $\frac{1}{20}$ and the rate in second week is also $\frac{1}{20}$ hence the situation is proportional.

(C)

To determine

To Make: The table showing the first week of savings for each girl.

Answer to Problem 16PPS

  

Explanation of Solution

Given: Suppose Isabel decide to save $\$20$ each week for her family. Her sister already has $\$10$ and wants to save $\$20$ each week.

  

The tabular form of the data is

  

(d)

To determine

To Find: The equation that represent the situation.

Answer to Problem 16PPS

For graph A: $y=20x+10$

For graph B: $y=20x$

Explanation of Solution

Given: Suppose Isabel decide to save $\$20$ each week for her family. Her sister already has $\$10$ and wants to save $\$20$ each week.

  

For the graph A

Slope is

  $\begin{array}{l}(x_1,y_1)=(0,10)\\ (x_{2,}{y}_2)=(1,30)\\ m=\frac{y_2-y_1}{x_2-x_2}=\frac{30-10}{1-0}=20\end{array}$

The slope of the line is $20$

Now

  $y$ Intercept is $10$

Thus

  $\begin{array}{l}y=mx+c\\ y=20x+10\end{array}$

Thus the equation of the line for the graph A is $y=20x+10$

Similarly

For the graph B

  $\begin{array}{l}(x_1,y_1)=(0,0)\\ (x_{2,}{y}_2)=(1,20)\\ m=\frac{y_2-y_1}{x_2-x_2}=\frac{20-0}{1-0}=20\end{array}$

The slope of the line is $20$

Now

  $y$ Intercept is $0$

Thus

  $\begin{array}{l}y=mx+c\\ y=20x\end{array}$

Thus the equation of the line for the graph B is $y=20x$