Most people have the mindset that the price of ethereum rises with bitcoin and vice versa. How true is this?
I think that depends. If we recall the end of 2017, we can see that Ethereum has risen in price, following bitcoin.
It depends on Bitcoin a lot. When the main cryptocurrency is starting to rise, Ethereum is also gaining, and vice versa. However, if BTC can add 10% (for instance), ETH can grow on 15% and even more.