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). When graphed, the function gives a line with a slope of 1.45 . If the monthly cost for 17 HCF is $46.36 , what is the monthly cost for 12 HCF?

Answer 1

A monthly bill cost 1.45 however 1.45×17 only equals 24.65 meaning there is a y intercept of 21.71. From there 1.45 times X (which in this case is 12) equals 17.40.
17.40 plus the y intercept (21.71) equals 39.11
Meaning for 12 monthes the cost is $39.11

Answer 2

We have to make the equation of this line;
Slope-point form: we need a point (x₀,y₀) and the slope (m).
y=mx +b
m=slope
b=y-intercept

We know the slope of the line (m=1.45) and we have a point (17 , 46.36). Therefore we need to calculate the y-intercept (b).
We plug in these values in the formula.
y=mx+b
46.36=1.45(17)+b
24.65+b=46.36
b=46.36-24.65
b=21.71

Therefore, now we know the y-intercept (b) and the slope (m).
The equation of the line will be:

y=1.45x+21.71

The question is:  What is the monthly cost for 12 HCF?
y=monthly cost
x=12
Therefore:
y=1.45(12)+21.71
y=17.4+21.71
y=39.11

Answer: the monthly cost would be $39.11