SOLUTION: Hi, could you please tell me how I would go about finding the solution to this problem: if f(2) = 3 and f(6) = 5, then what is f(10) ? Thank you very much!

Algebra ->  Functions -> SOLUTION: Hi, could you please tell me how I would go about finding the solution to this problem: if f(2) = 3 and f(6) = 5, then what is f(10) ? Thank you very much!      Log On


   

Question 568557: Hi,
could you please tell me how I would go about finding the solution to this problem:
if
f(2) = 3 and f(6) = 5, then what is f(10) ?
Thank you very much!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that this is a linear function. If f(2) = 3 and f(6) = 5, then the line has the points (2, 3) and (6, 5). So let's find the equation of the line that goes through these points.


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=2 and y%5B1%5D=3.
Also, is the second point . So this means that x%5B2%5D=6 and y%5B2%5D=5.


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


m=%285-3%29%2F%286-2%29 Plug in y%5B2%5D=5, y%5B1%5D=3, x%5B2%5D=6, and x%5B1%5D=2


m=%282%29%2F%286-2%29 Subtract 3 from 5 to get 2


m=%282%29%2F%284%29 Subtract 2 from 6 to get 4


m=1%2F2 Reduce


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


y-3=%281%2F2%29x%2B%281%2F2%29%28-2%29 Distribute


y-3=%281%2F2%29x-1 Multiply


y=%281%2F2%29x-1%2B3 Add 3 to both sides.


y=%281%2F2%29x%2B2 Combine like terms.


So the equation that goes through the points and is y=%281%2F2%29x%2B2


Therefore, the function is f%28x%29=%281%2F2%29x%2B2


Which means that


f%28x%29=%281%2F2%29x%2B2


f%2810%29=%281%2F2%29%2810%29%2B2


f%2810%29=10%2F2%2B2


f%2810%29=5%2B2


f%2810%29=7
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