Predicting heating cost with a downward-sloping line

Question

A home-energy model relates the monthly heating cost to the average outdoor temperature:

$\widehat{\text{cost}} = 250 - 3 \cdot (\text{temperature in }^\circ\text{F}).$

What heating cost does the model predict for a month averaging 40°F?

Accepted Answer

Substitute the input, 40^\circF, but mind the minus sign in front of the slope: \widehat{	ext{cost}} = 250 - 3 	imes 40 = 250 - 120 = 130 	ext{ dollars.} The slope is negative because warmer months need less heating, so the cost falls as temperature rises. Prediction still works exactly the same way: multiply the slope by the input, keeping its sign, then combine with the intercept. Here 3 	imes 40 = 120 is subtracted from the \250 baseline, giving \130. The one thing to watch with a downward slope is not to accidentally add when you should subtract; carry the negative through and the ari…

Predicting heating cost with a downward-sloping line

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