Question

the scatter plot shows the average monthly temperature, x, and the monthly heating cost of a family, y, for 24 different months. use the equation of the line of best fit, y = - 1.25x + 97.50, 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 °f? (b) what is the predicted heating cost for a month with an average temperature of 0 °f? (c) for an increase of one degree fahrenheit, what is the predicted decrease in the monthly heating cost?

Explanation:

Step1: Substitute value for (a)

Given $y = - 1.25x+97.50$, when $x = 25$, we substitute $x$ into the equation: $y=-1.25\times25 + 97.50$.
$y=-31.25+97.50$.
$y = 66.25$.

Step2: Substitute value for (b)

When $x = 0$, substitute $x$ into the equation $y=-1.25x + 97.50$.
$y=-1.25\times0+97.50$.
$y = 97.50$.

Step3: Analyze slope for (c)

The slope of the line $y=-1.25x + 97.50$ is $- 1.25$. This means for an increase of one - unit in $x$ (one degree Fahrenheit), the value of $y$ (monthly heating cost) decreases by $1.25$.

Answer:

(a) $\$66.25$
(b) $\$97.50$
(c) $\$1.25$