Christians, How do I identify a child of the bondwoman?

This passage is using Hagar (the bondwoman) and Sarah (the free woman) as analogies of law and grace. It is saying that if we are under the law, we will never measure up to God's standard and will be like the son of the bondwoman - unable to share in God's inheritance. But if we are under God's grace, we are like the free woman's son and able to share in the inheritance. This passage is reminding us that we are not to put ourselves under law because there is no promise for us there. We are to operate in accordance with the grace that God has given us today.