We consider a conservation law model of traffic flow, where the velocity v of each car depends on a weighted average of the traffic density rho(t,x) ahead. The averaging kernel is of exponential type: w(s)= (1/epsilon) exp(-s/ epsilon). By a transformation of coordinates, the problem can be reformulated as a 2 x 2 hyperbolic system with relaxation. Uniform BV bounds on the solution are thus obtained, independent of the scaling parameter epsilon. As epsilon approaches zero, the limit yields a weak solution to the corresponding conservation law rho_t + ( rho v(rho))_x=0. In the case where the velocity v is affine, say v(rho) = 1 – rho, using the Hardy-Littlewood rearrangement inequality we prove that the limit is the unique entropy-admissible solution to the scalar conservation law.