Question

The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using 14 HCF of water is $33.79, and the cost for using 27 HCF is $55.24. What is the cost for using 18 HCF of water?

Answer 1

The cost of using 18 HCF = $40.39

Explanation:

A linear function is one that has a constant rate of change for all the values within the distribution. For a linear function, there is a constant, and that constant is known as the slope or gradient of the linear function.

Let us first calculate this constant (slope).

Let:

X₁ = 14 HCF, Y₁ = $33.79, X₂ = 27 HCF, Y₂ = $55.24, m = slope

`m = (Y_2-Y_1)/(X_2 - X_1) \\m = (55.24 - 33.79)/(27-14) \\m = (21.45)/(13) \\m = 1.65`

at any two points on the linear function, the rate of change of the cost to HCF = 1.65

Now, Let X₃ = 18 HCF, Y₃ = cost for using 18 HCF

`m = (Y_3 - Y_1)/(X_3-X_1) \\where\ m= 1.65\\1.65 = (Y_3-33.79)/(18-14)\\1.65 = (Y_3 - 33.79)/(4) \\6.6 = Y_3 - 33.79\\Y_3 =6.6+33.79\\Y_3 = 40.39`

Therefore, the cost of using 18 HCF = $40.39

N:B X₂ and Y₂ can also be used with X₃ and Y₃ to find Y₃. You can try it out, you should get the same result