Expert: Steve Holleran - 8/26/2008

Question
input: 0, 1, 2, 3
output: 1, 7, 13, 19

input: 3, 6, 9, 12
output: 13, 28, 43, 58

Help me!!!!

Answer
Hi Nalani,

This is easier if you think of the data as ordered pairs:

I.  {(0,1) , (1,7) , (2, 13) , (3, 19)}

Pick any two points and find the slope : change in y / change in x

Lets use (1,7) and (2, 13)   (you can use ANY two)

    slope = m = 13 - 7 / 2 - 1 = 6 / 1 = 6

Now use y = mx + b ---> y = 6x + b .  Now pick any point, and put it in for x and y.  Lets use (0,1):

                       1 = 6(0) + b --> b = 1

so                      y = 6x + 1


II.  Same thing here.  Lets take (3,13) and (6,28):

    slope = m = 28 - 13 / 6 - 3 = 15 / 3 = 5

so   y = 5x + b    now lets us (3, 13) again for x and y:

   13 = 5(3) + b ----> 13 = 15 + b  so b = -2  and y = 5x - 2.


This will work every time as long as the data are linear.

Steve