How do we know Jesus is the branch mentioned in the Old Testament?

Throughout the Old Testament, prophetic texts such as Jeremiah 23:5-6 and Isaiah 11:1 link the title 'branch' to the coming of a righteous ruler from the lineage of David. In these contexts, the term 'branch' encompasses themes of kingship, righteousness, and priesthood, which culminate in the person and work of Jesus Christ. The New Testament affirms this identity by showcasing Christ's fulfillment of these roles, as He restores the broken relationship between God and humanity through His sacrificial death and resurrection.