SOLUTION: trying to create a formula for the following function table: x=1,2,3,4 and y=20,16,12,8. Appreciate any help, thank you!

Algebra ->  Functions -> SOLUTION: trying to create a formula for the following function table: x=1,2,3,4 and y=20,16,12,8. Appreciate any help, thank you!      Log On


   

Question 641379: trying to create a formula for the following function table: x=1,2,3,4 and y=20,16,12,8. Appreciate any help, thank you!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We have two points (1,20) and (2,16). Let's find the equation of the line through them.



First let's find the slope of the line through the points and


Note: is the first point . So this means that x%5B1%5D=1 and y%5B1%5D=20.
Also, is the second point . So this means that x%5B2%5D=2 and y%5B2%5D=16.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%2816-20%29%2F%282-1%29 Plug in y%5B2%5D=16, y%5B1%5D=20, x%5B2%5D=2, and x%5B1%5D=1


m=%28-4%29%2F%282-1%29 Subtract 20 from 16 to get -4


m=%28-4%29%2F%281%29 Subtract 1 from 2 to get 1


m=-4 Reduce


So the slope of the line that goes through the points and is m=-4


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-20=-4%28x-1%29 Plug in m=-4, x%5B1%5D=1, and y%5B1%5D=20


y-20=-4x%2B-4%28-1%29 Distribute


y-20=-4x%2B4 Multiply


y=-4x%2B4%2B20 Add 20 to both sides.


y=-4x%2B24 Combine like terms.


So the equation that goes through the points and is y=-4x%2B24

So the equation is y=-4x%2B24 which can be written as the function f%28x%29=-4x%2B24

As a check, plug in each given x value. You should get the corresponding y values given.