  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.
