Answer:
--- Sam
--- Tim
Step-by-step explanation:
Given
Sam Tim
х --- f(x) --------------- g(x)
1 --- 80 --------------- 100
2 --- 110 --------------- 120
3 --- 140 --------------- 140
4 --- 170 -------------- 160
Required
Determine the y value
y value implies the equation of the table
Calculating the equation of Sam
First, we need to take any corresponding values of x and y
![(x_1,y_1) = (1,80)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%281%2C80%29)
![(x_2,y_2) = (4,170)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%284%2C170%29)
Next, we calculate the slope (m)
![m = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
![m = \frac{170 - 80}{4 - 1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B170%20-%2080%7D%7B4%20-%201%7D)
![m = \frac{90}{3}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B90%7D%7B3%7D)
![m = 30](https://tex.z-dn.net/?f=m%20%3D%2030)
Next, we calculate the line equation using:
![y - y_1=m(x-x_1)](https://tex.z-dn.net/?f=y%20-%20y_1%3Dm%28x-x_1%29)
![y - 80 = 30(x - 1)](https://tex.z-dn.net/?f=y%20-%2080%20%3D%2030%28x%20-%201%29)
![y - 80 = 30x - 30](https://tex.z-dn.net/?f=y%20-%2080%20%3D%2030x%20-%2030)
Make y the subject
![y = 30x - 30 + 80](https://tex.z-dn.net/?f=y%20%3D%2030x%20-%2030%20%2B%2080)
![y = 30x +50](https://tex.z-dn.net/?f=y%20%3D%2030x%20%2B50)
Calculating the equation of Tim
First, we need to take any corresponding values of x and y
![(x_1,y_1) = (1,100)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%281%2C100%29)
![(x_2,y_2) = (4,160)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%284%2C160%29)
Next, we calculate the slope (m)
![m = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
![m = \frac{160 - 100}{4 - 1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B160%20-%20100%7D%7B4%20-%201%7D)
![m = \frac{60}{3}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B60%7D%7B3%7D)
![m = 20](https://tex.z-dn.net/?f=m%20%3D%2020)
Next, we calculate the line equation using:
![y - y_1=m(x-x_1)](https://tex.z-dn.net/?f=y%20-%20y_1%3Dm%28x-x_1%29)
![y - 100 = 20(x - 1)](https://tex.z-dn.net/?f=y%20-%20100%20%3D%2020%28x%20-%201%29)
![y - 100 = 20x - 20](https://tex.z-dn.net/?f=y%20-%20100%20%3D%2020x%20-%2020)
Make y the subject
![y = 20x - 20+100](https://tex.z-dn.net/?f=y%20%3D%2020x%20-%2020%2B100)
![y = 20x +80](https://tex.z-dn.net/?f=y%20%3D%2020x%20%2B80)