Find a and b when y= |x| and y= a|x+b| intersect?

If Y = a|x + b| passes through (-1, 0) and (0, 0.5), we have:

0.5 = a|0 + b|
a|b| = 0.5
ab = 0.5 or ab = -0.5

0 = a|-1 + b|
Note that a can't be zero (since a|b| = 0.5), so we divide through by a:
|-1 + b| = 0
b - 1 = 0
b = 1
a|1| = 0.5
1a = 0.5
a = 0.5