You filled in for your coworker while she was out on vacation last week. You had so much work to do while she was gone. She asks how it went, and you answer:
I was slammed all week.
To "be slammed" at work means to have a lot of work to do. The word "slam" is also used to describe the sound of a door being shut quickly, or of someone falling and hitting the floor. So you can imagine "being slammed" as having a large amount of work suddenly hit you while making a large sound.
"Slammed" is an ugradable adjective, like "horrible", "exhausted", "delicious", or "enormous". These are all words that have extreme meanings, so it seems strange to say that you were "very slammed" or "a little slammed".
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