Help with linear Interpolation formula

Introduction to linear interpolation formula

In the mathematical sub field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points. Linear interpolation is a method of curve fitting using linear polynomials. It is heavily employed in mathematics (particularly numerical analysis), and numerous applications including computer graphics. It is a simple form of interpolation.

Definition of Linear Interpolation Formula

The linear interpolation is the straight line between the two points which are given by the coordinates (x₀, y₀) and (x₁, y₁). In the interval of (x₀, x₁) the value of x which gives the straight line and it is given from the equation for the value of y along.
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It can be derived geometrically as follow

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