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$(x\_1,y\_1)$, the linear interpolant is the straight line between these points. For a value in the interval $(x\_0,\; x\_1)$, the value along the straight line is given from the equation of slopes

which can be derived geometrically from the figure on the right. It is a special case of polynomial interpolation with $n\; =\; 1$.

Solving this equation for , which is the unknown value at , gives

which is the formula for linear interpolation

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