In this chapter, Paul calls Timothy a "son" and his "child." Paul discipled Timothy as a Christian and a church leader. Paul may also have led him to believe in Christ. Therefore, Paul called Timothy his "son in the faith." (See: [[rc://en/tw/dict/bible/kt/disciple]], [[rc://en/tw/dict/bible/kt/faith]] and [[rc://en/tw/dict/bible/kt/spirit]] and [[rc://en/ta/man/translate/figs-metaphor]])
Genealogies are lists that record a person's ancestors or descendants. Jews used genealogies to choose the right man to become king. They did this because only a son of a king could normally become king. They also showed from what tribe and family they came. For example, priests came from the tribe of Levi and the family of Aaron. Most important people had records of their genealogies.
The phrase "the law is good if one uses it lawfully" ([verse 8](./08.md)) is a play on words. The English words "law" and "lawfully" come from the same root, and they translate words that come from the same root in the original language, so it would be well to translate the clause so as to preserve this word play.