  The aim of this paper is to compute the class of the closure of the effective
divisor in M_{6,1} given by pointed curves [C,p] with a sextic plane model
mapping p to a double point. Such a divisor generates an extremal ray in the
pseudoeffective cone of M_{6,1} as shown by Jensen. A general result on some
families of linear series with adjusted Brill-Noether number 0 or -1 is
introduced to complete the computation.
