Romans has been a book that uses comparisons. Some examples were Adam verses Jesus, grace verses the law, obedience verses disobedience, physical wealth verses spiritual wealth. In chapter 6, Paul takes on the issue of sin and compares it with freedom and slavery. Sin must not be a part of our lives. Sin wants to control us and become our master but we must confess and turn from our sin. In the logical conclusion when we dialog about sin, we know that when we sin we involve our bodies and there are consequences to sin that ripple to all parts of our lives, but if we present our bodies to God we are given life. There is the mistaken idea that because we are under grace and not under the law we have carte blanche to sin but that could not be further from the truth.
If a person is in slavery to another person, as a slave you must obey the master. In spiritual terms if sin is our master and we obey and sin it leads to death and if we do not follow sin our obedience leads to righteousness. Thanks be to God because once we were slaves to our sins but not we are obedient in our hearts we are no longer a slave to sin but we have become slaves to righteousness. It is not bondage it is freedom.