Question

suppose that a households monthly water bill (in dollars) is a linear function of the amount of water the household uses (in hundreds of cubic feet, hcf). when graphed, the function gives a line with a slope of 1.55. see the figure below.
if the monthly cost for 15 hcf is $44.17, what is the monthly cost for 21 hcf?

Explanation:

Step1: Define linear function form

Let $x$ = water usage (HCF), $C(x)$ = monthly cost. The linear function is $C(x) = mx + b$, where $m=1.55$ (slope).

Step2: Solve for intercept $b$

Substitute $x=15$, $C(15)=44.17$:
$$44.17 = 1.55(15) + b$$
$$44.17 = 23.25 + b$$
$$b = 44.17 - 23.25 = 20.92$$

Step3: Write full cost function

$$C(x) = 1.55x + 20.92$$

Step4: Calculate cost for 21 HCF

Substitute $x=21$:
$$C(21) = 1.55(21) + 20.92$$
$$C(21) = 32.55 + 20.92 = 53.47$$

Answer:

$\$53.47$