Final answer:
A curve with a shallow slope on a graph representing cosmological models would imply the largest current age of the universe, as it suggests a universe expanding over a longer period of time.
Step-by-step explanation:
The various curves on a graph that represent different cosmological models each imply a different current age of the universe. According to the given descriptions of the models, the curve with a shallow slope would imply the largest current age of the universe. This is because a shallow slope on such a graph suggests a universe that has been expanding for a longer period compared to universes represented by steeper curves. Specifically, Curve 2 in Figure 29.9, which represents a universe with a density lower than critical and will continue to expand but at an ever-slower rate, would suggest a universe that expands indefinitely, and hence, a greater age.