How do you visualize the graph of $(x - y)^2 = 4$ without a device?

Question

I can expand it to $x^2 - 2xy + y^2 = 4$, but that doesn't really help, and I cannot isolate the $y$ or $x$ term by itself because of the squared, so I would guess this to be some kind of parabolic shape, however it appears to be two parallel lines on a graphing device. Unless I choose a whole bunch of points and try to plot them, how do you quickly visualize this without a device?

Answer 1

Write it as $(x - y)^2 - 2^2 = 0$. This gives $(x - y - 2)(x - y + 2) = 0$. This is the union of two lines $x - y - 2 = 0$, $x - y + 2 = 0$. Find two points from each line to plot the graph.