Behind Vanessa Hyatt-Fugate’s home, down a weed-strewn slope in the Hollywood Hills subdivision off Thompson Bridge Road, runs Slaughterhouse Creek, a narrow, babbling stream that empties into a Lake Lanier cove. Undercut banks, exposed roots and downed trees reveal erosion’s heavy toll, a result of years of unmitigated stormwater runoff. In recent years, the flow of silt and sediment downstream from nearby developments and road construction prompted a dredging of the cove, costing local property owners nearly $200,000.