Chapter 4.2, Problem 4.27E

(a)

To determine

To identify the slope of the line and explain what it means in this setting.

Answer to Problem 4.27E

The slope of the line is $-19.87$ .

Explanation of Solution

The line given in the question is:

  $y=1425-19.87x$

The slope of the line is $-19.87$ .

This means that if the average monthly temperature increases by one, then the amount of natural gas consumed decrease by about $19.87$ .

(b)

To determine

To identify the $y$ intercept of the line and explain what it means in this setting.

Answer to Problem 4.27E

The $y$ intercept is the constant in the equation i.e. $1425$ .

Explanation of Solution

The $y$ intercept is the constant in the equation i.e. $1425$ .

This means that if the average monthly temperature is zero, then the amount of natural gas consumed decrease by about $1425$ .

(c)

To determine

To predict the amount of natural gas Joan will use in a month with an average temperature of ${30}^0\text{F}$ .

Answer to Problem 4.27E

The amount of natural gas Joan will use is about $1098.90$ .

Explanation of Solution

Now to calculate it, we should replace $x\text{ with }30$ in the equation of the line given in the question;

  $\begin{array}{l}y=1425-19.87x\\ \Rightarrow y=1425-19.87(30)\\ \Rightarrow y=1425-326.10\\ \Rightarrow y=1098.90\end{array}$

Thus the amount of natural gas Joan will use is about $1098.90$ .