[RPG] Can you cast a spell learned from the Magic Initiate feat using spell slots

Yes, you can use warlock slots to cast any spell you know. It's in the PHB in the section on multiclassing. Page 164:

If you have both the Spellcasting class feature and the Pact Magic class feature from the warlock class, you can use the spell slots you gain from the Pact Magic feature to cast spells you know or have prepared from classes with the Spellcasting class feature, and you can use the spell slots you gain from the Spellcasting class feature to cast warlock spells you know.

The effect is determined by the slot's level, as always in D&D 5e.

No; you can only use slots to cast lower-level spells from your class

The PHB rules (p. 164) for multi-class characters specifically address a multi-class character with slots of a level they can't "know or prepare". And it says You can use those slots, but only to cast your lower-level spells. It further elaborates that if any of those lower-level spells are improved by being used in a higher-level slot, you may get those benefits.

If this loophole worked, a similar loophole would exist for wizards: they can only prepare spells in their spellbook. And the rule for whether they can put a spell into their spellbook is only that the spell must be 'of a level for which [they] have spell slots'. So a multiclass wizard with an up-level slot can find a higher-level spell, and then could copy it into his book, and then prepare and cast it. RAI is pretty clear this won't work (after all, RAW explicitly says it won't, it just also kind of contradicts itself by implication).

In other words, the multi-class character rule saying you can't overrides normal rules for learning and casting spells. It is the "more specific" rule. The character may not 'know' or 'cast' spells higher level than their class levels allow. Which means your example wizard can't copy misty step into their spell book; that would constitute 'knowing' the spell. Nor could they prepare and cast it.