There is no strict relation between eth and btc. Just look at the charts of bitcoin and ethereum prices since the beginning of 2018 and you will see how different their paths are. https://imgur.com/a/6vFmp
However, when bitcoin is going down, people start feeling unsure about the market in general and thus the price of ethereum goes down as well. And eth's price is also really affected by ico bans, because it is the basic platform for icos.
Yet I disagree with the op that eth is dead. It still has chances to recover, even though for now mining it is really unprofitable, taking into account the fact of eth fork that makes eth closer to not being mineable at all.