how to dervie a linear function from a number table

Question

n --f(n)

1 --6

2--8

4--12

8--20

15--34

Answer 1

Think of the table as just a set of points (x, y) or, in this case (n, f(n) ). Find the slope by subtracting two f(n) values and dividing that number by the subtraction of the corresponding n values.

After you get the slope, either use the point-slope form of a line [ (y-y1) = m(x-x1) ] by plugging in the slope you calculated for the m and any one of the table points for the (x1, y1) point. Or use the slope intercept form [y = mx + b] by plugging in the m value you calculated and then plugging in any point for x and y and then solving for b.

I'd be happy to help explain this better if you'd like.