About Linear Interpolation Formula
The simplest way for predicting the value of a function between any two known values is to utilise the linear interpolation formula. The linear interpolation formula is also a handy tool for fitting curves with linear polynomials. Using a set of values, the interpolation method is used to find new values for any function.
What do you mean by Linear Interpolation Formula?
The linear interpolation method is utilised in data forecasting, data prediction, mathematical and scientific applications, and market research. Use the linear interpolation formula to discover the unknown values in the table. The linear interpolation formula is as follows:
Linear Interpolation(y) = y1+(x−x1)(y2−y1)/(x2−x1)
Linear Interpolation Formula
Linear Interpolation(y) = y1+(x−x1)(y2−y1)/(x2−x1)
where,
x1 and y1 are first coordinates
x2 and y2 are second coordinates
x is a point to perform interpolation
y is an interpolated value
Solved example based on Linear Interpolation Formula
Example: Find the value of y, if x = 6 and some set of values are given as (3, 4), (6, 8)?
Sol:x = 6 ; x1 = 3 ; x2 = 6 ; y1 = 4 ; y2 = 8 (given),
- Using the linear interpolation formula,
- Linear Interpolation(y) = y1+(x−x1)(y2−y1)/(x2−x1)
- Put the values,y=4+(6−3)(8−4)/(6−3)
- y = 4 + 3(4/3)
- y = 4 + 4
- y = 8
- Therefore, the value of y is 8.
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