Linear interpolation you need to know it

Linear interpolation is a procedure widely used to estimate the values that a function takes in a range of which we know its values at the extremes (x1, f (x1)) and (x2, f (x2)). 

To estimate this value we use the approximation to the function f (x) by means of a line r (x) (hence the name of linear interpolation, since quadratic interpolation also exists). The expression of the linear interpolation is obtained from the one-degree Newton interpolator polynomial.

 
LINEAR INTERPOLATION STRAIGHT 

Let's see the steps that we have to follow to find the regression line:

1. Given the points of the function (x1, y1) and (x2, y2), we want to estimate the value of the function at a point x in the interval x1 <x <x2. 

2. To find the line of interpolation we will look at the following image. 

For this we use the similarity of the ABD and CAE triangles, obtaining the following proportionality of segments: AB / AC = BD / CE. 

3. Clearing the segment BD (since the point D is the one that we do not know) we obtain: BD = (AB / AC) ∙ CE. Translating to algebraic language we obtain that: 

And clearing, we get:

The same expression that is obtained when using the interpolator polynomial of Newton that we had already commented. Remember that y1 = f (x1) and likewise y2 = f (x2). 

Look an example of where you can apply this procedure

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