SOLUTION: i am having trouble with finding the rule for the function x y 0 3 2 4 4 5 6 6 i have trouble in general with every problem but this is the one im really stuck

Algebra ->  Functions -> SOLUTION: i am having trouble with finding the rule for the function x y 0 3 2 4 4 5 6 6 i have trouble in general with every problem but this is the one im really stuck      Log On


   

Question 210183: i am having trouble with finding the rule for the function
x y
0 3
2 4
4 5
6 6
i have trouble in general with every problem but this is the one im really stuck on! thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's assume that there is a linear relationship. So this means that there's a line that goes through every point listed above.

To find the equation of the line, we only need two points. So let's use (0,3) and (2,4)




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=0 and y%5B1%5D=3.
Also, is the second point . So this means that x%5B2%5D=2 and y%5B2%5D=4.


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


m=%284-3%29%2F%282-0%29 Plug in y%5B2%5D=4, y%5B1%5D=3, x%5B2%5D=2, and x%5B1%5D=0


m=%281%29%2F%282-0%29 Subtract 3 from 4 to get 1


m=%281%29%2F%282%29 Subtract 0 from 2 to get 2


So the slope of the line that goes through the points and is m=1%2F2


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-3=%281%2F2%29%28x-0%29 Plug in m=1%2F2, x%5B1%5D=0, and y%5B1%5D=3


y-3=%281%2F2%29x-%281%2F2%29%280%29 Distribute


y-3=%281%2F2%29x%2B0 Multiply


y=%281%2F2%29x%2B0%2B3 Add 3 to both sides.


y=%281%2F2%29x%2B3 Combine like terms.


So the equation that goes through the points and is y=%281%2F2%29x%2B3


This line also goes through the other points listed above.


Note: To make a function, simply replace 'y' with 'f(x)' to get f%28x%29=%281%2F2%29x%2B3