Final answer:
The Waterfall model was the first life cycle model to gain wide acceptance among system developers. It is known for its linear and sequential approach, but has largely been supplanted by more flexible methodologies.
Step-by-step explanation:
The first life cycle model to gain wide acceptance among system developers was the Waterfall model.
The Waterfall model is a linear and sequential approach where each phase must be completed before the next phase can begin. The model was one of the earliest methodologies used and laid the foundation for structured systems analysis and design methods in software engineering. Its simplicity and ease of understanding made it widely accepted among developers during the early years of software development.
However, as software development evolved to require more flexibility, other models, such as the Evolutionary model and Agile methodologies, have surpassed the Waterfall model in popularity due to their iterative and adaptive nature.