Linear interpolation is a technique used to to fit an algebraic equation using linear polynomials. Long and short of it, it “assumes” that the rate of x-axis changes is directly proportional to the rate of change of y-axis.
What do I mean by that? See the diagram below.
c is a constant (could be zero to simply)
m is the gradient
It can also be simplified by using the following linear interpolation equation.
Graphically, it can be drawn as this.
Ok enough of math.
This is how we would write a RSlogix 5000 PLC logic using the linear interpolation equation above (without c constant). This technique is also known as scaling and is used to convert raw value (4 to 20 mA) to engineering unit (it could be kPa, psi, deg C, etc).
Wiki – Linear Interpolation