pt 
enGiven a pair of points $(x_{1},y_{1})$ e $(x_{2},y_{2})$, a linear interpolation represents the line that connects those points. For a new point $x^{\ast}$ inside interval $(x_{1},x_{2})$, the value $y^{\ast}$ is given by:
$\dfrac {y^{\ast}-y_{1}}{y_{2}-y_{1}}=\dfrac {x^{\ast}-x_{1}}{x_{2}-x_{1}}$
this could be found as shown in the following figure, as the line slope is constant. This is a special case of polynomial interpolation of unity order $(n = 1)$.
Solving for $y^{\ast}$ with $x^{\ast}$ we get:
$y^{\ast}=y_{1}+\dfrac {(y_{2}-y_{1})}{(x_{1}-x_{0})}(x^{\ast}-x_{1})=y_{2}-\dfrac {(y_{2}-y_{1})}{(x_{1}-x_{0})}(x_{2}-x^{\ast})$
this calculates the linear interpolation within the interval $(x_{1},x_{2})$. If $x^{\ast}$ is not inside the interval $(x_{1},x_{2})$, we call it linear extrapolation.