Concept

# Linear interpolation

Summary
In mathematics, 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. Linear interpolation between two known points If the two known points are given by the coordinates (x_0,y_0) and (x_1,y_1), the linear interpolant is the straight line between these points. For a value x in the interval (x_0, x_1), the value y along the straight line is given from the equation of slopes \frac{y - y_0}{x - x_0} = \frac{y_1 - y_0}{x_1 - x_0}, which can be derived geometrically from the figure on the right. It is a special case of polynomial interpolation with n=1. Solving this equation for y, which is the unknown value at x, gives \begin{align} y &= y_0 + (x-x_0)\frac{y_1 - y_0}{x_1 - x_0} \ &= \frac{y_0(x_1-x_0)}{x_1-x_0} + \fra
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