We don't know what A is for the given values of B, so we'll choose values of A that make it pretty simple.
(A, B) = (0, 5), (1, 7), (2, 9), (3, 11)
We note that when we subtract each B value from the next, we get 2. We also note that when we subtract each A value from the next, we get 1. So, B increases 2 times as fast as A.
So far, we have B = 2*A + (some constant).
For A = 0, we have B = 5, so the value of (some constant) must be 5.
B = 2A+5
Check
A = 1, B = 2(1) + 5 = 2+5 = 7 (yes)
A = 2, B = 2(2) + 5 = 4+5 = 9 (yes)
A = 3, B = 2(3) + 5 = 6+5 = 11 (yes)
If we want the A values to start with 1, ((1,5),(2,7), etc.) we can alter the rule in either of two ways.
(A, B) = (0, 5), (1, 7), (2, 9), (3, 11)
We note that when we subtract each B value from the next, we get 2. We also note that when we subtract each A value from the next, we get 1. So, B increases 2 times as fast as A.
So far, we have B = 2*A + (some constant).
For A = 0, we have B = 5, so the value of (some constant) must be 5.
B = 2A+5
Check
A = 1, B = 2(1) + 5 = 2+5 = 7 (yes)
A = 2, B = 2(2) + 5 = 4+5 = 9 (yes)
A = 3, B = 2(3) + 5 = 6+5 = 11 (yes)
If we want the A values to start with 1, ((1,5),(2,7), etc.) we can alter the rule in either of two ways.
- substitute (A-1) for A to get B = 2(A-1)+5 = 2A - 2 + 5 = 2A+3
- start with B=2A+(some constant) and compute a new constant. 5=2(1)+c; 5=2+c; 3=c; so B = 2A+3. This is the same result as above, of course.
