#### Linear Interpolation Formula

Interpolation is a method of finding new values for any function using the set of values. This formula is used to determine the unknown value at a given point. To calculate the new value from the two given points, we should use the linear interpolation formula. In comparison to Lagrange’s interpolation formula, the “n” set of numbers should be available and Lagrange’s method should be used to find the new value.

An interpolation is the process of finding a value between two points on a line or curve. If we remember what it means, we should consider the first part of the word, ‘inter,’ as meaning ‘enter,’ which reminds us to look ‘inside’ the information we started with. In addition to being useful in statistics, interpolation is also useful in science, business, or any time there is a need to predict values that fall between two existing data points.

**What is Linear Interpolation?**

A function can be interpolated by estimating its value between any two known values. A relationship is often present, and with the help of experiments at a range of values, other values are able to be predicted. The interpolation method can be useful for estimating the function of non-tabulated points. By interpolating, it is possible to estimate any desired value at some specific point at some known coordinate system.

When searching for a value between two points of data, linear interpolation can be beneficial. The mathematician therefore considers it as “filling in the gaps” for a given set of data values displayed in tabular format.The standard method of linear interpolation is the use of a straight line in order to connect the given points on both the positive and the negative side of the unknown data point.

For non-linear data, linear interpolation is not always an accurate method. In some cases, linear interpolation may not give a good estimate if the points in the data set change by a large amount. In addition to that, it involves estimating a new value by connecting two adjacent known values with a straight line.

**Linear Interpolation Formula:**

Linear interpolation is calculated as follows:

Linear Interpolation = y_{1 + }

This is the elements of linear formula. Here as follows:

- The first coordinates are x
_{1}and y_{1} - while the second coordinates are x
_{2}and y_{2} - where x represents the point for interpolation
- y represents the interpolated value

**Linear Interpolation Formula – Solved Example:**

**Question no1:** Find the value of y at x = 4 given some set of values (2, 4), (6, 7).

Solution: Based on the known values,

x=4x_{1 }=2x_{2 }=6y_{1 }=4; y_{2}=7

The interpolation formula is,

y=y_{1}+

i.e., y=4+

y = 112

**How Does Linear Interpolation Method Work?**

It is the simplest method for obtaining values between the data points that is linear interpolation. In this method, there are straight lines connecting the data points.

**What is the formula for finding the interpolation between two numbers?**

It is imperative to know this formula. The formula is y = y_{1} + ((x – x_{1}) / (x_{2} – x_{1})) * (y_{2} – y_{1}), where x_{1} and y_{1} are the coordinates below the known x value, and x2 and y_{2} are the coordinates above the known x value.

**What is the interpolation method?**

Mathematics interpolation is a method for constructing new data points within the range of a set of known data points that are discrete. The function can be simplified by interpolating some points from the original function to produce a simpler function that is still fairly close to the original.

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