Question

How is any equation of the form y= -x + b its own inverse?

Answer 1

write it as
x + y = b

now recall how you take the inverse.
Isn't your first step simply to switch around the x and y variables?
So what you you get ?

Answer 2

The same equation, just simply switched:

if you have

x+y= b, the inverse is y+x=b, which is the same thing and therefore its own inverse?

Thank you!