You are dead to sin because you died with Christ at the cross.
You are alive to Christ, because you rose with Him in His resurrection.
So don’t serve sin like a slave, since it leads to death; serve Christ, which leads to life.
How this is about Jesus/Application
We have to die to our old self and sin, before we can be a new creation, rising in Christ’s resurrection. God does this to us in regeneration, and gives us a heart to believe and repent - it isn't something we have to try to do on our own. When we repent of our sins, we need to count ourselves dead and alive in Christ. This is the first imperative, the first thing Paul tells us to do, in the whole book of Romans!