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
\(\begin{array}{l}y=y_{1}+\frac{\left(x-x_{1}\right)\left(y_{2}-y_{1}\right)}{x_{2}-x_{1}}\end{array} \)
Where,
\(\begin{array}{l}x_{1}\end{array} \)
and \(\begin{array}{l}y_{1}\end{array} \)
are the first coordinates\(\begin{array}{l}x_{2}\end{array} \)
and \(\begin{array}{l}y_{2}\end{array} \)
are the second coordinatesx is the point to perform the interpolation
y is the interpolated value.
Solved Examples
Question:Â Find the value of y at x = 4 given some set of values (2, 4), (6, 7)?
Solution:
Given the known values are,
x = 4 ; x1 = 2 ; x2 = 6 ; y1 = 4 ; y2 = 7
The interpolation formula is,
y =
\(\begin{array}{l}y_{1}\end{array} \)
+ \(\begin{array}{l}\frac{(x-x_{1})(y_{2}-y_{1})}{x_{2}-x_{1}}\end{array} \)
y = 4 + \(\begin{array}{l}\frac{(4-2)(7-4)}{6-2}\end{array} \)
y = 4 + \(\begin{array}{l}\frac{6}{4}\end{array} \)
y = \(\begin{array}{l}\frac{11}{2}\end{array} \)
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