What is the formula for linear interpolation?

The value of y in the linear interpolation equation is defined as a sum of y0 and the product of y differential (y1 – y0), multiplied by the ratio between differentials of x ((x – x0) divided by (x – x1)). This is a method of calculating the unknown value of y for any given x on the interval between two known points with coordinates (x0,y0) and (x1,y1).

The model assumes linear relationship between x and y variable throughout the interval and is valid only within the limits of that given interval. Beyond the known interval, linear extrapolation should be used instead.