depend on
Synonym discussion
Sense: phrasal verb/1
All four phrasal verbs express trust in someone or something, but they differ in register and strength. 'Rely on' is the closest synonym for 'depend on' and can replace it in most contexts. 'Count on' is more informal and suggests a personal, often emotional expectation — you count on a friend to keep a secret. 'Bank on' is informal and conveys strong confidence that something will happen, often with money-related imagery ('I'm banking on a bonus this year'). 'Lean on' implies needing emotional or practical support from someone during a difficult time, rather than routine trust. For everyday use, 'depend on' and 'rely on' are the safest choices; 'count on' works well in conversation, while 'lean on' suits personal struggles.
Etymology
'Depend' comes from Latin 'dependere', made up of 'de-' (down) and 'pendere' (to hang). The original image was of something hanging down from or hanging on something else — like a weight hanging from a hook. Over time this physical sense shifted to the abstract idea of one thing resting on another for support or being controlled by it. The preposition 'on' was added in English to form the phrasal verb 'depend on', which replaced the older 'depend of' by the 1600s.