Question

Bit confused about absolute values

Answer 1

Remember the definition of |x|. So |x| = x if x≥0 or -x if x<0.

Answer 2

You did change something though: you turned y into |y|. Doing that makes something like (1,-1) a solution because the absolute value turns the -1 positive. The four rays coming out of the origin in the graph are pairs like (1,1), (1,-1), (-1,1), and (-1,-1).

Answer 3

The graph of an equation is a plot of every point that makes the equation true. So you've allowed negative y's.