Question

suppose that a household’s 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 1.35. see the figure below. if the monthly cost for 24 hcf is $44.81, what is the monthly cost for 18 hcf? monthly cost (in dollars) 44.81 24 water usage (in hcf)

Explanation:

Step1: Recall linear function formula

The linear function is \( y = mx + b \), where \( m \) is slope, \( x \) is water usage, \( y \) is cost. Given \( m = 1.35 \), \( x = 24 \), \( y = 44.81 \). First, find \( b \).
Substitute into formula: \( 44.81 = 1.35 \times 24 + b \)

Step2: Calculate \( b \)

Compute \( 1.35 \times 24 = 32.4 \). Then \( 44.81 - 32.4 = b \), so \( b = 12.41 \).

Step3: Find cost for 18 HCF

Now use \( y = 1.35x + 12.41 \) with \( x = 18 \).
Calculate \( 1.35 \times 18 = 24.3 \). Then \( y = 24.3 + 12.41 = 36.71 \).

Answer:

\( \$36.71 \)