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 19 HCF of water is $38.10, and the cost for using 46 HCF is $82.65. What is the cost for using 21 HCF of water?
There must have been a fixed cost involved,
cost = a(HCD) + b
case 1:
38.10 = 19(HCD) + b
case 2:
82.65 = 46(HCD) + B
Subtract them:
44.55 = 27HCD
HCD = 1.65
sub back into 38.10 = 19(HCD) + b to find b
now you have the whole equation, plug in HCD = 21
so would the equation look like 38.10=19(21)+b ?
No
go back and find b
from
38.10 = 19(HCD) + b with HCD = 1.65
Then you will have
c = 19 * (HCD) + whatever b is
To find the cost for using 21 HCF of water, we can use the given information that the monthly cost of water use is a linear function.
Let's write the linear function in the form y = mx + b, where y represents the cost in dollars and x represents the amount of water used in HCF.
We are given two data points: (19, 38.10) and (46, 82.65).
Using the formula for the equation of a line (y = mx + b), we can determine the values of m and b.
First, let's find the slope (m) using the two data points:
m = (y2 - y1) / (x2 - x1) = (82.65 - 38.10) / (46 - 19) = 44.55 / 27 ≈ 1.65
Now, let's find the y-intercept (b) by substituting the values of m and one of the data points (x1, y1) into the equation:
y1 = mx1 + b
38.10 = 1.65 * 19 + b
38.10 = 31.35 + b
b = 6.75
So, the equation of the linear function representing the monthly cost of water use is:
y = 1.65x + 6.75
Now we can substitute x = 21 into the equation to find the cost for using 21 HCF of water:
y = 1.65 * 21 + 6.75
y = 34.65 + 6.75
y = 41.40
Therefore, the cost for using 21 HCF of water is $41.40.