Distance from the ionizing source vs. velocity offset for different emission lines (labeled) modeled in the SDSS spectrum. The distance is derived from the ionization level at which each ion has the peak of relative abundance. The red curve is a power-law fit of the form v_out = a × r^b + c with the best-fit slope b = 0.20 ± 0.07. The gray dashed line shows a curve with a slope fixed to b = 0.5, the value for a simple ballistic trajectory. The dotted green curves are taken from the analytic treatment of an expanding AGN-driven wind presented in Faucher-Giguère & Quataert (2012), for v_in = 0.1c, and central density n₀ = 10 (top) and n₀ = 100 (bottom) cm⁻³.