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Interpolation Calculator
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The straight line between the two known coordinates is called the linear interpolation. Interpolation Calculator calculates the unknown interpolated coordinate between the two known coordinates. Linear Interpolation is used in numerical analysis in math and various applications like computer graphics etc. Normally Linear Interpolation is called as Interpolation.

Interpolation Formula
y = $\frac{(y_{2} - y_{1})(x - x_{1})}{x_{2} - x_{1}}$ + y$_{1}$
Where,
x1 and y1 are the first coordinates
x2 and y2 are the second coordinates
"x" is the point to perform the interpolation
"y" is the interpolated value.


 

Steps for Linear Interpolation

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Step 1 :  

Observe the values of first coordinates, second coordinates and the value of "x" where interpolation performed.



Step 2 :  

Apply the formula:
Interpolated y value = $\frac{(y_{2} - y_{1})(x - x_{1})}{x_{2} - x_{1}}$ + y$_{1}$



Interpolation Examples

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  1. Calculate the value of y when x = 3 for the coordinates (3, 3) and (5, 6) by using Linear Interpolation Formula?


    Step 1 :  

    Given x1 = 3, y1 = 3, x2 = 5, y2 = 6 and x = 3



    Step 2 :  

    Interpolated y value = $\frac{(y_{2} - y_{1})(x - x_{1})}{x_{2} - x_{1}}$ + y$_{1}$
    y = $\frac{(6 - 3)(3 - 3)}{5 - 3}$ + 3
    y = 3



    Answer  :  

    Interpolated y value = 3



  2. Calculate the value of y when x = 5 for the coordinates (4, 2) and (6, 7) by using Linear Interpolation Formula?


    Step 1 :  

    Given x1 = 4, y1 = 2 x2 = 6, y2 = 7 and x = 5



    Step 2 :  

    Interpolated y value = $\frac{(y_{2} - y_{1})(x - x_{1})}{x_{2} - x_{1}}$ + y$_{1}$
    y = $\frac{(7 - 2)(5 - 4)}{6 - 4}$ + 2
    y = 3



    Answer  :  

    Interpolated y value = 4.5



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