depend on is a verb meaning "be contingent on". It carries 3 recorded senses.
be contingent on
“The outcomes rides on the results of the election”
“Your grade will depends on your homework”
put trust in with confidence
“she is someone you can really rely on when times get rough”
“you can rely on his discretion”
be dependent on, as for support or maintenance
“elderly parents often depend on their adult children”
Definitions, synonyms and semantic relations for depend on come from Princeton University’s WordNet. Commonness is measured against a corpus of everyday English. Full sources and licences.