Bitcoins value does indeed affect the price of all altcoins since BTC/AltCoin trading pairs are the most commonly used and is usually the standard go to exchange pair on all cryptocurrency exchanges. So can Altcoin break all the relationship from bitcoin and run as a independent currency.
they're all traded against bitcoin, which is one reason it affects the prices of all altcoins. Also often the news related to bitcoin are the news for other cryptocurrencies too, therefore the movements are similar