|x| is tricky but maybe I can tell you so that it's clear 4ever.
You have to look at when what's inside the absolute value iszero. In this case x=0. That easy. Then, you have to split the cases:
For x>= 0, you have y = -x+1,
For x<=0, you have y = -(-x) + 1 = x+1, because abs(x)=-x, if x<=0.
Notice that x=0 is included in either case, because |x| is continuous.
Then plot each line choosing a couple of points, notice that for one case you should choose x=-1, -2, or x=0, but not positive values, and the other way for the case with x>=0.
