  After fixing a marking (V, W) of a quasifuchsian punctured torus group G, the
complex length l_V and the complex twist tau_V,W parameters define a
holomorphic embedding of the quasifuchsian space QF of punctured tori into C^2.
It is called the complex Fenchel-Nielsen coordinates of QF. For a complex
number c, let Q_gamma,c be the affine subspace of C^2 defined by the linear
equation l_V=c. Then we can consider the linear slice L of QF by QF \cap
Q_gamma,c which is a holomorphic slice of QF. For any positive real value c, L
always contains the so called Bers-Maskit slice BM_gamma,c. In this paper we
show that if c is sufficiently small, then L coincides with BM_gamma,c whereas
L has other components besides BM_gamma,c when c is sufficiently large. We also
observe the scaling property of L.
