Answer:
It will take her 3 hours to read 120 pages.
Step-by-step explanation:
The number of pages read(y) after x hour can be modeled by a linear function in the following format:
![y = ax + b](https://tex.z-dn.net/?f=y%20%3D%20ax%20%2B%20b)
In which a is the number of pages read per hour and b is the initial number of pages read.
A straight line goes through (0, 0)
This means that when ![x = 0, y = 0](https://tex.z-dn.net/?f=x%20%3D%200%2C%20y%20%3D%200)
So
![y = ax + b](https://tex.z-dn.net/?f=y%20%3D%20ax%20%2B%20b)
![0 = a*0 + b](https://tex.z-dn.net/?f=0%20%3D%20a%2A0%20%2B%20b)
![b = 0](https://tex.z-dn.net/?f=b%20%3D%200)
(0.5, 20)
When ![x = 0.5, y = 20](https://tex.z-dn.net/?f=x%20%3D%200.5%2C%20y%20%3D%2020)
So
![y = ax](https://tex.z-dn.net/?f=y%20%3D%20ax)
![20 = 0.5a](https://tex.z-dn.net/?f=20%20%3D%200.5a)
![a = \frac{20}{0.5}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B20%7D%7B0.5%7D)
![a = 40](https://tex.z-dn.net/?f=a%20%3D%2040)
The function in:
![y(x) = 40x](https://tex.z-dn.net/?f=y%28x%29%20%3D%2040x)
According to the graph, which statement must be true?
It will take her 2 hours to read 60 pages.
![y(2) = 40*2 = 80](https://tex.z-dn.net/?f=y%282%29%20%3D%2040%2A2%20%3D%2080)
Less than 2 hours for 60 pages, so this is false.
It will take her 3 hours to read 120 pages.
![y(3) = 40*3 = 120](https://tex.z-dn.net/?f=y%283%29%20%3D%2040%2A3%20%3D%20120)
This statement is true.
It will take her 4 hours to read 180 pages.
![y(4) = 40*4 = 160](https://tex.z-dn.net/?f=y%284%29%20%3D%2040%2A4%20%3D%20160)
More than 4 hours to read 180 pages. So false.
It will take her 5 hours to read 210 pages.
![y(5) = 40*5 = 200](https://tex.z-dn.net/?f=y%285%29%20%3D%2040%2A5%20%3D%20200)
More than 5 hours to read 210 pages. So false.