Slavery of sin is a metaphor meaning having such a strong desire to sin that one is unable to stop himself from sinning. It is as if sin controls the person. AT: "you were like slaves of sin" or "you were controlled by sin" (See: [[rc://en/ta/man/translate/figs-metaphor]])
Here the word "heart" refers to having sincere or honest motives for doing something. AT: "but you truly obeyed" (See: [[rc://en/ta/man/translate/figs-metonymy]])
Here "pattern" refers to the way of living that leads to righteousness. The believers change their old way of living to match this new way of living that Christian leaders teach to them. You can translate this in an active form. AT: "the teaching that Christian leaders gave you" (See: [[rc://en/ta/man/translate/figs-activepassive]])