Finite Differences and Linear Models

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I'm studying for an exam and as I have been attempting to work this problem, I realized I don't know what I'm doing. I have a Linear Finite Differences table, but my answers are way wrong.. would someone please remind me of how to get started? I found the slope and that the data has a first difference (and should be a linear model), but that's as far as I got. I tried to find b, but my solutions so far don't match the answer, so I'm guessing I am doing it wrong. Thanks in advance!

Finite differences model: Use finite differences to find a model for the following data, where x is the independent variable and y is the dependent variable.

X | Y
0 | 2
1 | 5
2 | 8
3 | 11
4 | 14



-- Alena
 
Subtract successive values for 'y', making sure the x's are sorted and have the same spacing.

Code: 
X | Y    First Difference
0 | 2 
1 | 5         5-2 = 3
2 | 8         8-5 = 3
3 | 11       11-8 = 3
4 | 14      14-11 = 3
 
Hey.. thanks for replying. I got that far, but not sure how to proceed to find the model.




-- Alena
 
The first differences are all the same so it is generated by a first order equation
y=ax+b
Since you have y(0)=2, b=2
Since you have y(1)=5, a+2=5, a=3
The equation is y=3x+2

If the second differences were all the same it would be generated by a second order equation
y=ax²+bx+c
and could be solved the same way.
etc.
 
Great.. thank you SO much! I knew it should be really simple, but I kept drawing a blank on it. Thanks again, Gene! :)



-- Alena
 
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