Final answer:
The Agricultural Adjustment Administration (AAA) was the agency created by FDR that regulated the farming industry, which, among other things, slaughtered millions of pigs and compensated farmers for not planting crops to reduce agricultural output and stabilize prices.
Step-by-step explanation:
The agency created by FDR that regulated the farming industry and was responsible for the elimination of thousands of pigs, and paying farmers to leave their fields fallow was the Agricultural Adjustment Administration (AAA). The AAA was part of Roosevelt's New Deal legislation aimed at addressing the agricultural crisis during the Great Depression by reducing agricultural overproduction and thereby increasing crop prices. The AAA did so by offering direct payments to farmers in exchange for reducing their crop production, a strategy intended to boost prices and alleviate rural poverty. Unfortunately,
this resulted in the controversial destruction of existing crops and livestock, including the slaughter of millions of pigs, to reduce the surplus and stabilize prices. However, over time the AAA adjusted its approach to purchase crops and meat which were then distributed to families in need.