Can an Arcane Trickster or Eldritch Knight with the Magic Initiate feat (picking the wizard list) use spell slots to cast the chosen 1st-level spell? [duplicate]

Question

A bard who takes the Magic Initiate feat and chooses the bard spell list for the feat can use spell slots to cast the 1st-level spell they learn from the feat. A wizard who takes the feat and chooses the wizard list can do the same.

Can an Arcane Trickster rogue or Eldritch Knight fighter who takes the Magic Initiate feat and picks the wizard spell list also use their spell slots to cast the 1st-level spell they pick for the feat?

Both the AT rogue and the EK fighter use the wizard spell list for their Spellcasting feature, so one could assume that they could use their spell slots to cast a wizard spell from the feat... But is that assumption correct?

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This Q&A addresses the general case:
Can you cast a spell learned from the Magic Initiate feat using spell slots?

However, the Arcane Trickster rogue and Eldritch Knight fighter are a bit of an exception and aren't specifically addressed by that Q&A. Both the Arcane Trickster rogue and Eldritch Knight fighter use the wizard spell list, even though they are not themselves wizards. As a result, I'm not 100% sure if my assumption about their interaction with the feat is correct.

Answer 1

Yes, this works.

In particular, casting a spell with your spell slots as an Eldritch Knight or Arcane Trickster requires two things: you know the spell, and it is a wizard spell. The spell gained from Magic Initiate (Wizard) satisfies both of these conditions.

Magic Initiate says:

Choose a class: bard, cleric, druid, sorcerer, warlock, or wizard. You learn two cantrips of your choice from that class’s spell list.

In addition, choose one 1st-level spell to learn from that same list. [...]

The Eldritch Knight's Spellcasting feature says:

The Eldritch Knight Spellcasting table shows how many spell slots you have to cast your wizard spells of 1st level and higher. To cast one of these spells, you must expend a slot of the spell’s level or higher. You regain all expended spell slots when you finish a long rest.

For example, if you know the 1st-level spell shield and have a 1st-level and a 2nd-level spell slot available, you can cast shield using either slot.

Similarly, the Arcane Trickster's spellcasting feature says:

The Arcane Trickster Spellcasting table shows how many spell slots you have to cast your wizard spells of 1st level and higher. To cast one of these spells, you must expend a slot of the spell’s level or higher. You regain all expended spell slots when you finish a long rest.

For example, if you know the 1st-level spell charm person and have a 1st-level and a 2nd-level spell slot available, you can cast charm person using either slot.

Since you know the spell from Magic Initiate, and it is a wizard spell, it meets all the conditions for being able to expend spell slots to cast it as an Eldritch Knight or an Arcane Trickster.

This ruling is confirmed in the Sage Advice Compendium:

In short, you must follow your character’s normal spellcasting rules, which determine whether you can expend spell slots on the 1st-level spell you learn from Magic Initiate.

See my answer to the more general question for more details.