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).

Question

When graphed, the function gives a line with the slope of 1.65. If the monthly cost 16 HCF is $48.37, what is the monthly cost for 22 HCF?

Answer 1

Hi Randa,

We can use the given information to write an equation of the function.

Let's use slope-intercept form, y = mx + b.

We know the slope is 1.65. And since 16 HCF costs $48.37, we have a point on the line. (16, 48.37)

Plugging this information into our equation, we get:

48.37 = 1.65 (16) + b

Multiply

48.37 = 26.4 + b

Subtract 26.4 form both sides

21.97 = b

Now if we put this into y= mx + b form along with our slope, we have:

y = 1.65x + 21.97

If we want to know how much 22 HCF costs, we just have to plug that into our equation as the x-value.

y= 1.65 (22) + 21.97

Simplify

y = 58.27

So 22 HCF would cost $58.27.

Answer 2

HI Randa,

I hope that you are doing well, during this weird time; and that this message finds you in a good place.

To get you started on this problem, you will want to think about how to go about graphing this linear function. You want to keep in mind that you want to plot your dependent variable on the y-axis, as it changes with respect to your independent variable (plotted on the x-axis). In this problem, the cost of the water bill depends on the amount of water used, in HCF. So the graph should be plotted with cost on the y-axis, and HCF on the x-axis.

It follows that you are given the coordinates of (16, $48.37) and (22, y₂); where y₂ represents the cost when using 22 HCF. You are also given the slope of your line (m, in y = mx + b format). You may recall that you can set-up a slope as the change in y over the change in x, or the "rise over the run" [m = (y₂-y₁) / (x₂-x₁)]. We can set this problem up, using this equation to solve for y₂ (the cost at 22 HCF) algebraically.

So we would set up the problem as 1.65 = (y₂-48.37)/(22-16). We then solve by combining like-terms and using inverse operations as follows:

1.65 = (y₂ - 48.37) / 6

1.65(6) = y₂ - 48.37

9.9 = y₂ - 48.37

y₂ = $58.27

I hope that this is helpful. Feel free to reach out if you need more help!

Best,

Ray

Answer 3

Lets start with constructing a dummy equation for this scenario, given only the slope:

f(x)=1.65*X+C

We know that the function must be dependent on the size of the house, as it outputs a water bill,

So, we can plug in the first values, and solve for C.

f(16)=48.37, which means: 48.37=1.65*16+C.

We solve for C her by subtracting 1.65*16 from both sides. We then get C=21.97.

Using this value, we then solve for the case of 22 HCF.

f(22)=1.65*22+21.97=58.27

So the new water bill for 22 HCF is $58.27 .