Algorithm to map an interval to a smaller interval

Question

I tried searching, but due to the nature of my question, I was unable to find something satisfactory.

My problem is the following: I am trying to map numbers ranging fro

Answer 1

To map
[A, B] --> [a, b]

use this formula
(val - A)*(b-a)/(B-A) + a

as correctly mentioned in the other answer it's linear mapping.

Basically

y = m*x + c

c = intersection at y-axis
m = slope determined by two known point (A, a), (B, b) = (b-a)/(B-A)