Question

use the equation of the line of best fit, $y = -1.23x + 97.30$, to answer the questions below. give exact answers, not rounded approximations.
(a) what is the predicted heating cost for a month with an average temperature of $25^{circ}f$?
(b) what is the predicted heating cost for a month with an average temperature of $0^{circ}f$?
(c) for an increase of one degree fahrenheit, what is the predicted decrease in the monthly heating cost?

Explanation:

Step1: Substitute \(x = 25\) into the equation \(y=-1.23x + 97.30\)

$$
LATEXBLOCK0
$$

Step2: Calculate the value of \(y\) for \(x = 25\)

$$y = 66.55$$

Step3: Substitute \(x = 0\) into the equation \(y=-1.23x + 97.30\)

$$y=-1.23\times0+97.30=97.30$$

Step4: Analyze the slope of the line \(y=-1.23x + 97.30\)

The slope \(m=-1.23\). In the context of the linear equation \(y = mx + b\), when \(x\) (temperature) increases by 1, \(y\) (heating cost) changes by \(m\).

Answer:

(a) \(\$66.55\)
(b) \(\$97.30\)
(c) \(\$1.23\)