Any of the terms could be zero.  Put in standard form of y=mx+b (where possible), we have:

x = 0

y = 0

y = -x

y = -x/2

y = -2x

So, 10  regions from 5 lines each of which goes through the origin.

Curiously, when plotted in Desmos, the y = -x line does not show up making it look like 8 regions unless you delete either the (x + y) term or the (y + x) term.

https://www.desmos.com/calculator/yro9ypzry0

But Wolfram Alpha gets it right.

So in this case, Wolfram beats Desmos and Matlab