Chapter 8.3, Problem 45STP

(a)

To determine

To calculate: To describe the linear relationship between number of cubic feet and weight of water.

Answer to Problem 45STP

The linear relationship is that weight of water is $64$ times the number of cubic feet of water

Explanation of Solution

Given information: The equation $y=64x$ describes the weight $y$ of $x$ cubic feet of water

Calculation:

Given the equation that describes the weight $y$ of $x$ cubic feet of water is as follows:

  $y=64x$

Here, weight of water is $64$ times the number of cubic feet of water

Conclusion:

Hence, the linear relationship is that weight of water is $64$ times the number of cubic feet of water

(b)

To determine

To calculate: To make a table of values that describe the relationship

Answer to Problem 45STP

Table is

Number of cubic feet of water	Weight of water
1	64
2	128
3	192
4	256

Explanation of Solution

Given information: The equation $y=64x$ describes the weight $y$ of $x$ cubic feet of water

Calculation:

Given the equation that describes the weight $y$ of $x$ cubic feet of water is as follows:

  $y=64x$

When $x=1$

  $\begin{array}{l}y=64\left(1\right)\\ y=64\end{array}$

When $x=2$

  $\begin{array}{l}y=64\left(2\right)\\ y=128\end{array}$

When $x=3$

  $\begin{array}{l}y=64\left(3\right)\\ y=192\end{array}$

When $x=4$

  $\begin{array}{l}y=64\left(4\right)\\ y=256\end{array}$

Hence, table is

Number of cubic feet of water	Weight of water
1	64
2	128
3	192
4	256

Conclusion:

Hence, table is created

(c)

To determine

To calculate: To explain the meaning of two ordered pairs

Answer to Problem 45STP

  $\left(1,64\right)$ represents that when number of cubic feet of water is $1$ , then weight of water is $64$

  $\left(2,128\right)$ represents that when number of cubic feet of water is $2$ , then weight of water is $128$

Explanation of Solution

Given information: The equation $y=64x$ describes the weight $y$ of $x$ cubic feet of water

Calculation:

Given the equation that describes the weight $y$ of $x$ cubic feet of water is as follows:

  $y=64x$

Hence, table is

Number of cubic feet of water	Weight of water
1	64
2	128
3	192
4	256

Let us consider the ordered pair $\left(1,64\right)$ and

  $\left(1,64\right)$ represents that when number of cubic feet of water is $1$ , then weight of water is $64$

  $\left(2,128\right)$ represents that when number of cubic feet of water is $2$ , then weight of water is $128$

Conclusion:

Hence, $\left(1,64\right)$ represents that when number of cubic feet of water is $1$ , then weight of water is $64$

  $\left(2,128\right)$ represents that when number of cubic feet of water is $2$ , then weight of water is $128$

(d)

To determine

To calculate: To graph the ordered pairs and a draw a line through them

Answer to Problem 45STP

Graph is sketched

Explanation of Solution

Given information: The equation $y=64x$ describes the weight $y$ of $x$ cubic feet of water

Calculation:

Given the equation that describes the weight $y$ of $x$ cubic feet of water is as follows:

  $y=64x$

Hence, table is

Number of cubic feet of water	Weight of water
1	64
2	128
3	192
4	256

Plotting the points in graph:

  

Conclusion:

Hence, graph of ordered pair is sketched