London, May 4 (BridgeNews) - Business activity in the euro-zone's service sector slowed to an index reading of 53.0 in April, from an unrevised 53.4 in March, according to sources with access to the region's latest survey of purchasing managers in the sector. This is the lowest reading since January 1999, but still above the key 50 level, which marks the barrier between contraction and expansion in output.