I think gradual emancipation is the most likely answer. Many states, like New York, passed laws ending slavery gradually (slave owners, even in what we typically call "free" states, had significant political clout). In New York's case, children born after July 4th, 1799 would be freed on their 25th birthday (for women) or 28th (for men). The state later passed a law emancipating people born before this date, which is why the number in the chart you posted drops off by about 1840.

Here's an excerpt from Eric Foner's Gateway to Freedom that goes in to a little more detail.