Linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points.

See linear model below.

In engineering application, this is especially helpful to convert 4 to 20mA into engineering units. Take for example the linear curve below. It basically means that, when 4mA is present, it denotes that it is 10kPa and when a current of 20mA is present, it means that the pressure is now 100kPa. You can calculate what does 10mA denote using the formula below.

What if you need to do a reverse linear interpolation?. That is to say, if you have 20mA it is 10kPa and 4mA will be 100kPa. The sketch below outlines what the curve will look like and how to calculate it.

I hope it helps all my fellow engineers out there with these notes. Cheers!