Linear Interpolation Formula Linear Interpolation Formula In numerical analysis that is part of mathematics there is used a term interpolation that is used for finding or making the new terms or points in the range of the data set of points but these points are not define in the discrete set of the data . Sometimes there is need of finding the data or points that is not the part of data set by doing sampling or observations or experiments that helps in finding the points in the given range of data set . So there is requirement of some technique that is known as the interpolation .Interpolation is the method of finding the intermediate value of independent variable. It is not the approximation of the points that is based on the given points in the data set that means it will helps in finding the real value for a point that is not the part of the data set .there is some techniques of the interpolation that are curve fitting, regression analysis etc. There is one type of interpolation that is known as the linear interpolation that is also defined as the way of searching the holes in the tables .
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It will be understand by an example as if we find the pressure on the given temperature and there is a table define that define the pressure on the different temperature means if at 40' centigrade pressure is 7.9 psk and at 45 ' centigrade it is 8 .7 psk and we want to find the pressure on 42 ' centigrade that is not directly define in the table so it will not find by the approximation but it will be find through the interpolation . Interpolation is define in terms of expression as if there are given coordinate points are (x1 , y1) and (x2 , y2) then according to the linear interpolation at point x for interval (x1 , x2) , value of y within the straight line define as Linear Interpolation Formula y – y1 / x – x1 = y2 - y1 / x2 – x1 . So according to this formula find the value of unknown y at the given point x as : y = y1 + (x – x1) y2 – y1 / x2 – x1 or y = y1 + ((x – x1) y2 – (x – x1) y1) / x2 – x1 . It have some very useful application that is used in fill the gaps in the table it will be defined as if there are some tables that define the population of some country in year 1980, 1990, 2000 and 2010 and if we want to find the population of that country in year 1994 then easiest way of finding the population of given year is linear interpolation. In computer graphics interpolation also used that is also called as the lerp that fields the jargon means it is used in finding the jargons between the two end points of a line. If we talk about the interpolation of data set points that define as (x0 , y0) , (x1 ,y1) …. then for finding the value of some data points it will used the concatenation operation of linear interpolation for each pair of data points that is used in relates the continuous curves of discontinuous derivatives .
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Example 2: Using the linear interpolation formula, find the equation for the given coordinates (6, 8) and (10, 16) Solution: Given coordinate values are (x0, y0) and (x1, y1) are (6, 8) and (10, 16). y = y0 + (x- x0) y1−y0x1−x0 y = 8 + (x -6) 16−810−6 y = 8 + (x - 6) (8/4) y = 8 + (x - 6)(2) y = 8 + 2x - 12 y = 2x -12 + 8 y = 2x - 4 2x -y = 4 (or) 2x - y - 4 = 0.
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