Answer:
The monthly cost for 9 HCF is $38.54
Step-by-step explanation:
<em>The graph is missing; however, the question can still be solved</em>
Given
Slope = 1.55
When monthly cost = $47.84, Amount of water = 15 HCF
Required
Determine the monthly cost for 9 HCF
From the question, we understand that it is a linear function;
Linear functions are of the form
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
Where y is the function of x and m is the slope
In this case; the function is the monthly water bill
and x is the amount of water
Solving for b
When monthly cost = $47.84, Amount of water = 15 HCF
The function is as follows;
![47.84 = 1.55 * 15 + b](https://tex.z-dn.net/?f=47.84%20%3D%201.55%20%2A%2015%20%2B%20b)
![47.84 = 23.25 + b](https://tex.z-dn.net/?f=47.84%20%3D%2023.25%20%2B%20b)
Subtract 23.25 from both sides
![47.84 - 23.25= 23.25 - 23.25 + b](https://tex.z-dn.net/?f=47.84%20-%2023.25%3D%2023.25%20-%2023.25%20%2B%20b)
![24.59 = b](https://tex.z-dn.net/?f=24.59%20%3D%20b)
![b = 24.59](https://tex.z-dn.net/?f=b%20%3D%2024.59)
Solving for the monthly cost for 9 HCF
Here, we have that
![x = Amount\ of\ water = 9](https://tex.z-dn.net/?f=x%20%3D%20Amount%5C%20of%5C%20water%20%3D%209)
![m = Slope = 1.55](https://tex.z-dn.net/?f=m%20%3D%20Slope%20%3D%201.55)
![b = 24.59](https://tex.z-dn.net/?f=b%20%3D%2024.59)
Substitute these values in the linear function; ![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
![y = 1.55 * 9 + 24.59](https://tex.z-dn.net/?f=y%20%3D%201.55%20%2A%209%20%2B%2024.59)
![y = 13.95 + 24.59](https://tex.z-dn.net/?f=y%20%3D%2013.95%20%2B%2024.59)
![y = 38.54](https://tex.z-dn.net/?f=y%20%3D%2038.54)
<em>Hence, the monthly cost for 9 HCF is $38.54</em>