Is there any function that does a linear interpolation using lists?

Question

Is there any function that does a linear interpolation using lists?

Something where I could report a list with a number of any, as below:

data = {{161 + 15, 0}, {x1, 525 - 18}, {103.4, 525}}

$\left( \begin{array}{cc} 176 & 0 \\ \text{x1} & 507 \\ 103.4 & 525 \\ \end{array} \right)$

Some function that actually does the following interpolation procedure:

x1=data[[1,1]]+((data[[3,1]]-data[[1,1]])/(data[[3,2]]-data[[1,2]]))*data[[2,2]]

105.889

Answer 1

As our friend @Shadowray said in the comments

data = {{161 + 15, 0}, {x1, 525 - 18}, {103.4, 525}};

Rescale[
 data[[2, 2]], {data[[1, 2]], data[[3, 2]]}, {data[[1, 1]], 
  data[[3, 1]]}]

105.889

The image below presents the idea of Rescale: