We study quintessence and phantom field theory models based on linear-negative potentials of the form V ( \phi ) = s \phi .
We investigate the predicted redshift dependence of the equation of state parameter w ( z for a wide range of slopes s in both quintessence and phantom models .
We use the gold dataset of 157 SnIa and place constraints on the allowed range of slopes s .
We find s = 0 \pm 1.6 for quintessence and s = \pm 0.7 \pm 1 for phantom models ( the range is at the 2 \sigma level and the units of s are in \sqrt { 3 } M _ { p } H _ { 0 } ^ { 2 } \simeq 10 ^ { -38 } eV ^ { 3 } where M _ { p } is the Planck mass ) .
In both cases the best fit is very close to s \simeq 0 corresponding to a cosmological constant .
We also show that specific model independent parametrizations of w ( z ) which allow crossing of the phantom divide line w = -1 ( hereafter PDL ) provide significantly better fits to the data .
Unfortunately such crossings are not allowed in any phantom or quintessence single field model minimally coupled to gravity .
Mixed models ( coupled phantom-quintessence fields ) can in principle lead to a w ( z ) crossing the PDL but a preliminary investigation indicates that this does not happen for natural initial conditions .