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Linear Interpolation Formula

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.

Formula of Linear Interpolation

\[\large y=y_{1}+\frac{\left(x-x_{1}\right)\left(y-y_{1}\right)}{x_{2}-x_{1}}\]

$x_{1}$ and $y_{1}$ are the first coordinates
$x_{2}$ and $y_{2}$ are the second coordinates
x is the point to perform the interpolation
y is the interpolated value.

Solved Examples

Question: Find the value of y at x = 4 given some set of values (2, 4), (6, 7)?


Given the known values are,
x = 4 ; x1 = 2 ; x2 = 6 ; y1 = 4 ; y2 = 7

The interpolation formula is,

y = $y_{1}$ + $\frac{(x-x_{1})(y_{2}-y_{1})}{x_{2}-x_{1}}$

y = 4 + $\frac{(4-2)(7-4)}{6-2}$

y = 4 + $\frac{6}{4}$

y = $\frac{11}{2}$


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