1. The problem asks: What does the y-intercept of the line tell you about the situation? 2. The y-intercept of a line on a graph is the point where the line crosses the y-axis. This happens when the x-value (time) is 0. 3. From the graph description, the line crosses the y-axis at $y=12$ miles per hour. 4. This means that at time $0$ seconds, Beth's speed was $12$ miles per hour. 5. In the context of the situation, the y-intercept represents Beth's initial speed before she started slowing down her bicycle. 6. Therefore, the y-intercept tells us the starting speed of Beth's bicycle at the beginning of the observed time interval. Final answer: The y-intercept indicates that Beth's initial speed at time $0$ seconds was $12$ miles per hour.