Chapter 1.6, Problem 12PPS

a.

To determine

To construct: The table which represents x as minutes and y as no. of times the person breathes.

Answer to Problem 12PPS

  $\begin{array}{cc}\text{minutes}\left(x\right)& \begin{array}{l}\text{no}.\text{ of times the}\\ \text{person breathes}\left(y\right)\end{array}\\ 1& 20\\ 2& 40\\ 4& 80\\ 8& 160\\ 10& 200\end{array}$

Explanation of Solution

Given information:

Person breathes 20 times per minute.

Formula:

No. of times person breathes=minutes $*20$ .

Consider the statement that Person breathes 20 times per minute.

Recall that No. of times person breathes=minutes $*20$ .

Therefore in $1$ minute person breathes about $20$ minutes.

Therefore no. of times person breathes $=1*20=20$ .

No. of times person breathes $=2*20=40$ .

No. of times person breathes $=4*20=80$ .

No. of times person breathes $=8*20=160$ .

No. of times person breathes $=10*20=200$ .

Therefore the ordered pair table is

  $\begin{array}{cc}\text{minutes}\left(x\right)& \begin{array}{l}\text{no}.\text{ of times the}\\ \text{person breathes}\left(y\right)\end{array}\\ 1& 20\\ 2& 40\\ 4& 80\\ 8& 160\\ 10& 200\end{array}$ .

b.

To determine

To graph: To graph the scatter plot of the data mentioned above.

Answer to Problem 12PPS

  

Explanation of Solution

Given information:

The ordered table is mentioned below.

  $\begin{array}{cc}\text{minutes}\left(x\right)& \begin{array}{l}\text{no}.\text{ of times the}\\ \text{person breathes}\left(y\right)\end{array}\\ 1& 20\\ 2& 40\\ 4& 80\\ 8& 160\\ 10& 200\end{array}$

Formula:

Use the ordered pair from the table mentioned above.

Graph:

The graph plotted below is a scatter plot on which minutes represents x axis and no. of times person breathes represents y axis.

  

Interpretation:

Considered the ordered pair of the table mentioned above.

Recall that x axis represents minutes and y axis represents no. of times person breathes.

Now we use the ordered pair table for the points to be plot.

Therefore we get the scatter plot as mentioned above.

c.

To determine

To write: An equation which relates the x and y where x represents minutes and y represents no. of times person breathes.

Answer to Problem 12PPS

The algebraic equation relating x and y is $y=20*x$.

Explanation of Solution

Given information:

The ordered pair table is mentioned below.

  $\begin{array}{cc}\text{minutes}\left(x\right)& \begin{array}{l}\text{no}.\text{ of times the}\\ \text{person breathes}\left(y\right)\end{array}\\ 1& 20\\ 2& 40\\ 4& 80\\ 8& 160\\ 10& 200\end{array}$

Formula:

x represents minutes and y represents no. of times person breathes.

Consider the ordered pair table as mentioned above.

Recall that x represents minutes and y represents no. of times person breathes.

Therefore person breathes $20$ times per $1$ minute.

Therefore $y=20*x$ where y represents no. of times person breathes and x represents minutes.