the scatter plot shows the average monthly temperature, x, and the monthly heating cost of a family, y, for…

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?

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?

Answer

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$