Linear Interpolation

 It is a estimation of a function (as a logarithm) by assuming that it is a straight line between known value.Linear interpolation is a method of curve fitting using linear polynomials.

Graphically :

Connect two data points with a straight line



Given two points (x0, y0) and (x1, y1), the linear polynomial passing through the two points is the equation of the line passing through the points. One way to write its formula is


Note :

If f(x) = ex, then f(.82)  2.270500, f(.83)  2.293319, and f(.826)  2.2841638. Note then that P1(x) is an approximation of f(x) = ex for x 2 [.82, .83].

In general, if y0 = f(x0) and y1 = f(x1) for some function f, then P1(x) is a linear approximation of f(x) for all x ε  [x0, x1].


Examples:  For the data points (2, 3) and (5, 7) find P1(x).