If not, when it is ? Can the make it a function to understand the nature of the formula ?

No.
If y is larger than x the relation is not satisfied.

“When is it satisfied?” can be addressed with some simple algebra. But you need to show you’ve tried to solve it first; we don’t just do homework problems for others. That doesn’t help anyone learn

Is this homework ?

It is not homework. I was thinking about it and can't seem to find a situation there it is incorrect. This equation surely tells interesting things when graphed.

@MigL

When X>Y

10-4 = 6

|Y-X| =| -6| = 6

When Y>X

4-10 = -6

|10-4|=6

Ok lets modify, when Y>X, |X-Y| =|Y-X|

Yes
Ix-yI=Iy-xI

and ???

@MigL What is the law called ? Seems useful but never taught

30 minutes ago, HbWhi5F said:

@MigL What is the law called ? Seems useful but never taught

The law of the bleedin’ obvious?

On 9/8/2025 at 6:36 AM, HbWhi5F said:

@MigL What is the law called ? Seems useful but never taught

These are commutative properties.

A+B = B+A

Google it and you will the algebraic explanations.

On 9/8/2025 at 7:07 AM, exchemist said:

The law of the bleedin’ obvious?

You bad man....

When you start dealing with matrices these things do not necessarily commute so it is good that these distinctions are stated. At least he is asking questions.

I'll just add this

https://en.m.wikipedia.org/wiki/Commutative_property

The equation x - y = |y - x| is only true under specific conditions. It holds true when x ≥ y, because: - If x ≥ y, then (y - x) ≤ 0 - The absolute value |y - x| = -(y - x) = x - y - So the equation is satisfied However, when y > x: - Then x - y is negative - But |y - x| is always positive - So they are NOT equal In summary: x - y = |y - x| if and only if x ≥ y