Although she forgot to water it for a week, the plant was still alive/live.
Which one is right?
My professor has just told me that you must use ALIVE. But I don't know why yet.
For OP's specific context, alive and live are effectively synonyms (meaning living, not dead). The main difference is that, as OED points out, alive occurs chiefly in predicative use (after a verb)...
This animal is alive
...as opposed to adjectival live, used attributively (before a noun) in the semantically equivalent...
This is a live animal
Note that this distinction only applies in contexts where the living sense is both literal and specifically focusses on gross physical attributes, such as the ability to act/move autonomously. Thus, for example,...
...are both relatively "standard" usages. Attributive use of alive is uncommon, so no-one is likely to say "This is alive yoghurt" in any context. But if we consider these two alternatives...
1: This cheese is live
2: This cheese is alive
...most people would interpret #1 the same as the yoghurt examples (i.e. - the micro-organisms which made the cheese in the first place are still living within it). But #2 would probably be interpreted as a facetious allusion to a very mature, runny Camembert, slithering around the plate like a living thing. Or perhaps a truly disgusting cheese as per the more "figurative" usage...
I'm not eating that! It's alive with maggots!
...where alive implies visibly moving in and on it (also crawling with maggots), again with the "whole living organism" sense.
Where the sense is even more figurative (live = real-time, not recorded, for example), live is normally used in both contexts...
This news report is live (being broadcast as events happen)
It's a live news report (has exactly the same meaning).
TL;DR: OP's teacher is quite correct - native speakers would normally say is alive when they literally mean has not [yet] died, because it's an "attributive" usage.
So your sentence is
Although she forgot to water it for a week, the plant was still __
In the blanks you have to place an adjective, that is apparent. And to fill in the blank you have two alternatives - alive and live
Now consider the two words and how it's used in that meaning. It will help you choose the correct one to fill in the blank.
Live - (adj - Used only before a noun) Not dead or inanimate; living
- A live animal
- A live match
(N.B - There are other meaning and usage for "live" that you can find in dictionary. But I just mentioned this one as it's relevant to your original sentence.)
Alive - (adj) Living and not dead. (Here in dictionary entry nothing was mentioned about its position in reference to noun or whatever it will qualify. But you will learn that it's used not before noun, instead after that.)
- Hopes of finding anyone still alive were fading
- He was kept alive by a feeding tube
Now it's very clear which one to use to fill in the blank in your sentence. As "live" in this sense is only used before noun or whatever/whoever it describe, so we can't use in this case "live". So we can go for "alive". And this is the correct usage.
Correct sentence -
Although she forgot to water it for a week, the plant was still alive.
Let me add that this is an unusual case. Usually we use the same adjective before a noun as we use in a predicate. For example, "The flag is red. The red flag waved." "The man is hungry. The hungry man ate dinner." But with live/alive, there are two different forms. "The dog is alive. The live dog ran away."
"Live" can be used as a predicate adjective when we are not talking about a creature but about a machine. "The telephone line is live now." "Be careful -- that wire is live."
At the moment I can't think of another adjective that has different forms for these two cases. Can anyone think of other examples?