Final answer:
Olivia's efforts to motivate Sarah into a leadership role align with the Path-Goal Theory, which focuses on defining goals and showing how to achieve them.
Step-by-step explanation:
Olivia's meeting with Sarah to get her interested in a leadership role would likely align with the Path-Goal Theory of leadership. This theory is concerned with a leader's ability to motivate subordinates to achieve a set of goals and to provide a path for them to follow. It is proactive, aimed at empowerment, and seeks to clarify the path to various rewards by defining roles, tasks, and the means to achieve them. Compared to the other leadership theories listed, Path-Goal Theory best explains the proactive effort by Olivia to motivate Sarah into a leadership role by possibly discussing the rewards, the goals, and how Sarah's abilities can help achieve them.