In the context, Paul is exhorting the Corinthians to live holy and pure lives because they now belong to Jesus.
The Corinthians were guilty of many sins, such as taking brothers in Christ to unbelieving judges and suing them, engaging in lustful and sexual immorality and other sins of the flesh that cut on off from God.
Paul makes it abundantly clear that man is a slave of Christ due to the phrase "you were brought at a price", giving us the implication that one is subject to Christ in all his life and that we are to live to him and die to sin and live for righteousness.
Being a slave of Christ doesn't mean that we are partakers of apartheid and subject to it, but we have our will to be inexorably bound to his (His way or the highway to put it bluntly).
This is why Jesus tells us to deny ourselves, take up the cross and follow him, it is his will that is to be accomplished, not mans.
By all means see if it is the Lords Will for you to do something and if there isn't a direct command, do what should please him, which includes listening to your conscience if you feel uncertain about a particular activity, movie, what you can read etc.
Let us give ourselves to the cause of Christ with no hesitation.