Finding level curves of function with absolute value

Question

I'm trying to find the level curves that correspond to this function:

I know that the first step is to set the function equal to a random k, and after that try different values to see if it looks similar to a known equation but I haven't been able to make much progress beyond that. Thanks for any help!

Answer 1

Here they are... pretty straightforward:

or...

Answer 2

That just gives you $$|x| + y=c$$ or, rewritten, $$y = c - |x|.$$ Surely you know what this looks like for various values of $c$?