Level curve of min function

Question

So I was trying to graph level curves using derivatives. I can't seem to understand how to graph this type of function through derivatives. Haven't found assistance for this anywhere, so can I get help on how to derive level curves of $f(x,y) = min \{ax,by\}$

Answer 1

The minimum of $ax$ and $by$ is one of these terms. The level curves of $ax$ and $by$ are axis-aligned straight lines. They meet where the terms are equal.