Thank you for the Biblical question on location, “Scripture tells of Joseph’s brothers going to Egypt to buy food because of a severe famine in their land. Where did his brothers and his father Jacob live?”
As one reads the biblical narrative, Jacob moved away from Esau and initially lived in Shechem, to Bethel where he built an altar to the LORD God, to Ephrath (Bethlehem) and Kiriath Arba or Hebron. The text states that this was where Abraham and lived.
Genesis 35 says this, “Jacob came home to his father Isaac in Mamre, near Kiriath Arba (that is, Hebron), where Abraham and Isaac had stayed. 28 Isaac lived a hundred and eighty years. 29 Then he breathed his last and died and was gathered to his people, old and full of years. And his sons Esau and Jacob buried him” (NIV).
The text further states that Jacob and his children left their place of encampment and journey to Beersheba where he made an altar to the LORD God (Gen. 46:1).
SUMMARY: Jacob and his children encamped around the area of Hebron where there were grass for their herds and the location of his childhood.
For further insight and discussion: