Final answer:
The South agreed to the Fugitive Slave Clause in the Constitution to protect their economic interests and ensure the return of runaway slaves. This clause provided federal support for the return of slaves and protected the property rights of slaveholders.
Step-by-step explanation:
The South would agree to the Fugitive Slave Clause in the Constitution because it provided a constitutional protection for slavery and mandated federal support for the return of runaway slaves. The clause ensured that slaves who escaped to the North would be returned to their owners in the South, thus protecting the economic interests of slaveholders. By including this provision, the South had the assurance that their property rights would be respected and their labor force would not be depleted.