Dependency is directional. Starting a car is dependent on petrol. But petrol is not dependent on starting a car.
What word describes the relationship from petrol to the car?
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Does this answer your question? Does "associated with" imply a certain hierarchy? – Edwin Ashworth Aug 27 '21 at 18:30
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Related: Does 'associated with' imply a certain hierarchy? – Edwin Ashworth Aug 27 '21 at 18:31
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requisite (n., adj.)
A necessary or indispensable thing; something needed for a particular purpose.
All the requisites for living are there if you take the time to look. OED
ADJECTIVE
You can use requisite to indicate that something is necessary for a particular purpose.
[formal]
She filled in the requisite paperwork.
Synonyms: necessary, needed, required, called forCOUNTABLE NOUN
A requisite is something that is necessary for a particular purpose[formal]
An understanding of accounting techniques is a requisite for the work of the analysts. Collins
If you really need something opposite to dependency, requisiteness does exist:
The fact of being requisite; necessity, need.
Focusing on the preexisting social facticity of possessive individualism..and its requisiteness to the functioning of market society. OED
... and with arguing that certain sorts of relationships are 'requisite' in terms of the tasks which have to be achieved. There is no systematic evidence in terms of which such claims as to the requisiteness of the advocated patterns can be tested... R. K. Brown; Understanding Industrial Organizations
DjinTonic
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You hinted at one yourself with "directional." The phrase "unidirectional relationship" seems to be used mainly in the fields of computing logic (and apparently psychology?), but has exactly the definition you give. For a more informal equivalent, you could just say "one-way relationship."
Andy Bonner
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This seems to be a comment on the wording of the question, rather than an answer to it. – jsw29 Aug 27 '21 at 16:05
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Really? Sorry, perhaps I was unclear. "Unidirectional relationship" or "one-way relationship" express what the OP is looking for (to a T, it seems to me). – Andy Bonner Aug 27 '21 at 16:22
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The OP was looking for a word that can fill the blank in 'If starting a car is dependent on petrol, then petrol is ____ for starting a car'. – jsw29 Aug 28 '21 at 15:49
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@jsw29 Sorry, I took it differently. "What word describes the relationship." I take it they're looking for an adjective that modifies the relationship, not the petrol. – Andy Bonner Aug 28 '21 at 16:54
