Zooming that graph out to start in 1980 shows that there is a trend there that did not start in 2009 but closer to 2000.

Also, that specific graph is of limited utility because it is the over-16 labor force participation rate, not the prime-age one. Which means that as the age distribution skews more toward post-retirement-age people it will automatically drop. Which is exactly what's been happening, by the way, as the baby boomers have started retiring. This rate will also drop as more people go to college instead of starting work immediately after high school.

https://www.bls.gov/opub/ted/2017/employment-population-rati... has a chart that lets you see a breakdown by age group, sort of, for 2007-2017. Note the huge differences in the rate between the age buckets and where the overall rate falls compared to the 25-54 rate.