This can be stated in active form. Alternate translation: "These are the things concerning Israel that God revealed to Amos, one of the shepherds in Tekoa" (See: [[rc://en/ta/man/translate/figs-activepassive]])
The words "in the days of" is an idiom and refers to the time when each king reigned. Alternate translation: "when Uzziah was king of Judah, and also when Jeroboam son of Joash was king of Israel" (See: [[rc://en/ta/man/translate/figs-idiom]])
The assumed knowledge is that the original hearers would be aware of when a large earthquake had affected the area. (See: [[rc://en/ta/man/translate/figs-explicit]])