Final answer:
Southwest Airlines is the airline headquartered at Love Field in Dallas. It is recognized for its low-cost carrier model and has grown substantially since its establishment in 1967.
Step-by-step explanation:
The airline that is headquartered out of Love Field in Dallas is Southwest Airlines. Love Field serves as the corporate headquarters and an operating base for Southwest, which is known for its low-cost carrier model and extensive domestic network. This airline was established in 1967 by Herb Kelleher and Rollin King, and it has grown to become one of the largest airlines in the United States, famous for its vibrant corporate culture and strong customer service ethos.