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). Whengraphed, the function gives a line with a slope of 1.65. See the figure below.If the monthly cost for 16 HCF is $49.67, what is the monthly cost for 11 HCF?

Answer 1

Given:

The function gives a line with a slope of 1.65.

The monthly cost for 16 HCF is $49.67.

Required:

To find the monthly cost for 11 HCF.

Explanation:

The slope-intercept form of line is

$y=mx+b$

We know the slope is 1.65.

And since 16 HCF costs $49.67, we have a point on the line. (16, 49.67)

Plugging this information into our equation, we get:

$\begin{gathered} 49.67=1.65(16)+b \\ \\ b=49.67-26.4 \\ \\ b=23.27 \end{gathered}$

Now

$y=1.65x+23.27$

If we want to know how much 11 HCF costs, we just have to plug that into our equation as the x-value.

$\begin{gathered} y=1.65(11)+23.27 \\ \\ y=18.15+23.27 \\ \\ y=41.42 \end{gathered}$

Final Answer:

The monthly cost for 11 HCF is $41.42