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 $ 32.68 , and the cost for using 52 HCF is $ 95.38 . What is the cost for using 19 HCF of water?

Answer 1

$40.93

Explanation:

Given

Linear function of:

• 14 HCF = $32.68
• 52 HCF = $95.38

To find:

• 19 HCF = ?

Solution

Linear equation in slope-intercept form:

• y(x) = mx +b

We have points of: (14, 32.68), (52, 95.38):

• y(14) = 14 m + b
• y(52) = 52 m +b

Using the points we can find the value of m and b:

• m= (y2-y1)/(x2-x1)
• m= (95.38 - 32.68)/(52 - 14)
• m = 62.7/ 28
• m= 1.65

Then finding b:

• 14*1.65 +b = 32.68
• b= 32.68 - 23.1
• b= 9.58

So the function is:

• y = 1.65 x + 9.58

Then y(19) is found as:

• y(19) = 1.65*19 + 9.58
• y(19) = 40.93

Answer: Cost of 19 HCF of water is $40.93