Question

the scatter plot shows the average monthly temperature, x, and the monthly heating cost of a family, y, for 25 different months. use the equation of the line of best fit, y = - 1.25x + 98.50, to answer the questions below. give exact answers, not rounded approximations. (a) for an increase of one degree fahrenheit, what is the predicted decrease in the monthly heating cost? (b) what is the predicted heating cost for a month with an average temperature of 0 °f? (c) what is the predicted heating cost for a month with an average temperature of 45 °f?

Explanation:

Step1: Analyze slope for part (a)

The equation of the line is $y = - 1.25x+98.50$. The slope is - 1.25. For a one - unit increase in $x$ (temperature), the change in $y$ (cost) is equal to the slope. So the predicted decrease in cost is $1.25$ dollars.

Step2: Substitute $x = 0$ for part (b)

Substitute $x = 0$ into $y=-1.25x + 98.50$. Then $y=-1.25\times0 + 98.50=98.50$.

Step3: Substitute $x = 45$ for part (c)

Substitute $x = 45$ into $y=-1.25x + 98.50$. So $y=-1.25\times45+98.50=-56.25 + 98.50 = 42.25$.

Answer:

(a) $1.25$
(b) $98.50$
(c) $42.25$