Linear interpolation is a mathematical curve fitting technique. The goal of linear interpolation is to take known data points and create new data points as estimations based upon known values. For example, suppose we know that a car starts at a velocity of 0 miles per hour (mph). After 1,000 feet, we use a laser to clock the speed of the car at 60 mph. If we assume a constant rate of acceleration (linear), then we could use linear interpolation to estimate the speed of the car after 10 feet, 20 feet, 30 feet, and so on. Even though we only know the speed of the car at 0 feet and 1,000 feet, we can estimate the speed at any distance traveled between 0 and 1,000 feet using linear interpolation.
The formula for linear interpolation solved for an unknown variable y (think of this as the speed of the car in the example) can be given as follows:
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