adjective
a word that describes or modifies a noun or pronoun, in this case 'teachy' describes something that is related to teaching or giving instruction
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The professor's teaching style was very informative and not at all teachy.
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I don't like it when teachers get all teachy and preachy during class.
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Stop being so teachy, just let me figure it out on my own!
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Her constant corrections were starting to feel a bit teachy, like she was trying to show off her knowledge.