Final answer:
The branch of Christianity that emerged in Egypt is Coptic Christianity, which became independent following the Council of Chalcedon in 451 due to the adoption of the Monophysite position over Christ's nature.
Step-by-step explanation:
The branch of Christianity that emerged in Egypt is Coptic Christianity. After the Council of Chalcedon in 451, a significant group within the Egyptian Christian community adhered to the Monophysite position, which maintained that Christ's humanity was inseparable from his divinity. Rejecting the Dyophysite position decreed by the council, this group became more isolated from the wider Christian world and formed an independent path, becoming known as the Coptic Church. It recognized Coptic as both the major literary language and the language of public worship in Egypt.