The NY City Council yesterday approved the first major overhaul of the most popular tax break for apartment building developers, adopting a plan intended to induce them to build tens of thousands of apartments for people other than the wealthy. The changes, which Mayor Michael R. Bloomberg supported and which would go into effect in 2008, significantly increase the areas of the city in which developers who want the tax break must make one of every five apartments they build affordable to lower-income people. The boundaries of those areas would be reconsidered every two years in light of trends in the housing market.