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

 


Practise This Question

Appu’s father plans on opening an Anthurium flower farm. He read that Anthurium plants require soils with good water absorption capacity along with good aeration. He has three choices: Clayey soil, Sandy Loam soil and coco peat (an artificial soil made from coconut husks). He took 50g of each soil and determined the volume of water it absorbed. He also determined the soil particle size using a microscope and tabulated the results.

Soil TypeVolume of water absorbed by 50g of soilParticle sizeClayey35 mL0.002 mmSandy Loam15 mL1 mmCoco Peat350 mL1 mm

Which soil should Appu’s father choose?