Home prices in most U.S. cities increased at a slower pace in October from September, as higher mortgage rates weighed on sales and dampened the housing recovery, an index showed Tuesday. The Standard & Poor's/Case-Shiller 20-city home price index rose 0.2 percent from September to October, down from a 0.7 percent increase from August to September. Monthly price gains slowed in 18 of the 20 cities tracked by the index, and prices declined in nine cities, including Chicago, Denver, and Washington. For the year, prices are still strong, reflecting big gains in earlier months. They have risen 13.6 percent over the past 12 months, the fastest since February 2006. The Case-Shiller index covers roughly half of U.S. homes. It is not adjusted for seasonal variations, so the change partly reflects slower buying in the fall.