What is the main difference between this two equations : y=-2x and y=|-2x| ?

y=|-2x| looks like two different equations:
When
x>=0: y=2x
x<0: y=-2x
|| is a magnitude operator that makes it’s parameter positive. y=-2x is a straight line, starting from the top left, passing (0,0). y=|-2x| will bounce that off the x axis.
What is the main difference between this two equations : y=-2x and y=|-2x| ?
What is the main difference between this two equations : y=-2x and y=|-2x| ? 

the magnitude operator is || so y = |-2x| = positive data 2x , x=>0 to y=> 2x
and normal -2x , x=>0 to y=> -2x
Computational mathematics need to study
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