# Program to implement Linear Extrapolation

• Difficulty Level : Basic
• Last Updated : 23 Jun, 2022

What is Extrapolation?
Extrapolation is the process in mathematics where the required value is estimated beyond the range the of the given variable range. Extrapolation is often used to estimate the data of some observation below or above the given range. Extrapolation is also referred to as a mathematical prediction to predict values by observing the relationship between the given variables. There are many processes of Extrapolation.Here only Linear Extrapolation will be discussed. This process was first described by Thomas D. Clareson in 1959 in his book of science. He referred to it as a meaningful prediction by understanding the given data.
How to calculate Linear Exptrapolation?
The method is useful when the linear function is given. It is done by drawing a tangent and extending it beyond the limit. Linear Extrapolation gives a very good result when the point to be predicted is not very far from the rest of the points.

Extrapolation formula: Here and are two given points and x is the point for which we want to predict the value of y.
Examples:

Input:  , x = 1.2
Output: y = 3.15 Implementation:

## C++

 // C++ code for the implementation// of Linear extrapolation #include using namespace std; // Consider a structure// to keep each pair of x and y togetherstruct Data {    double x, y;}; // Function to calculate// the linear extrapolationdouble extrapolate(Data d[], double x){    double y;    y = d.y        + (x - d.x)              / (d.x - d.x)              * (d.y - d.y);     return y;} // Driver Codeint main(){    // Sample dataset    Data d[] = { { 1.2, 2.7 }, { 1.4, 3.1 } };     // Sample x value    double x = 2.1;     // Finding the extrapolation    cout << "Value of y at x = 2.1 : "         << extrapolate(d, x);     return 0;}

## Java

 // Java code for the implementation of// Linear extrapolationclass GFG{     // Function to calculate the linear// extrapolationstatic double extrapolate(double[][] d, double x){    double y = d + (x - d) /                (d - d) *                (d - d);     return y;} // Driver Codepublic static void main (String[] args){     // Sample datasetdouble[][] d = {{ 1.2, 2.7 },{ 1.4, 3.1 }}; // Sample x valuedouble x = 2.1; // Finding the extrapolationSystem.out.println("Value of y at x = 2.1 : " +                    extrapolate(d, x));}} // This code is contributed by chandan_jnu

## Python3

 # Python3 code for the implementation of# Linear extrapolation # Function to calculate the linear# extrapolationdef extrapolate(d, x):    y = (d + (x - d) /        (d - d) *        (d - d));     return y; # Driver Code # Sample datasetd = [[ 1.2, 2.7 ], [1.4, 3.1 ]]; # Sample x valuex = 2.1; # Finding the extrapolationprint("Value of y at x = 2.1 :",             extrapolate(d, x)); # This code is contributed by mits

## C#

 // C# code for the implementation of// Linear extrapolationclass GFG{     // Function to calculate the linear// extrapolationstatic double extrapolate(double[,] d, double x){    double y = d[0,1] + (x - d[0,0]) /                (d[1,0] - d[0,0]) *                (d[1,1] - d[0,1]);     return y;} // Driver Codestatic void Main(){     // Sample datasetdouble[,] d = {{ 1.2, 2.7 },{ 1.4, 3.1 }}; // Sample x valuedouble x = 2.1; // Finding the extrapolationSystem.Console.WriteLine("Value of y at x = 2.1 : " +                    extrapolate(d, x));}} // This code is contributed by chandan_jnu

## PHP

 

## Javascript

 

Output:

Value of y at x = 2.1 : 4.5

Time Complexity: O(1)

Auxiliary Space: O(1)

My Personal Notes arrow_drop_up