Problem:
Given the following points:
$A(0,1,3),B(-4,3,8),C(-5,4,9),D(-6,2,1)$
How can the function of the line $f(x, y)$ be determined?
Attempts:
I've tried looking for adaptations of LaGrange's interpolation formula, however the only applications are for 2 dimensional coordinates (it seems). I did find a link which looked promising; unfortunately, it looks like it only applies for two points?
If you are looking for the equation of a line passing through four points, it does not always work out.
A line is determined by just two points. The other points may or may not be on that line.
However you can use the least square method to fit a line to your data which may or may not pass through the points.
The linear regression is a common process to fit a line through a set of points.