I am wondering about different methods for plotting real valued functions of two variables manually. So far I have encountered 2 methods:
Using contour maps and setting one of the variables to 0 and plotting the one dimensional graph of the other variable, and vise versa
Using a suitable variable substitution
I have not managed to find a clear explanation specifying a method of how one should go about drawing functions of two variables. Is method 1 the best way to go about it? And does method 2 always works?
For instance if one wants to graph the function $\textit{f}$(x, y)= ln($x^{2}$+$y^{2}$), both methods work and one can use the substitution $r^{2}$=$x^{2}$+$y^{2}$ which would give the function $\textit{f}$(r)= 2 ln r.
But what would be a suitable variable substitution for f(x,y)=x +2y -2? (which represents a plane)
Any help would be greatly appreciated!