# 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

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

Where,

$x_{1}$ 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)?

**Solution:**

Given the known values are,

x = 4 ; x_{1} = 2 ; x_{2} = 6 ; y_{1 }= 4 ; y_{2} = 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 = $\frac{11}{2}$