  In this paper, we consider the connectedness of planar self-affine set
$T(A,\mathcal{D})$ arising from an integral expanding matrix $A$ with
characteristic polynomial $f(x)=x^2+bx+c$ and a digit set
$\mathcal{D}=\{0,1,\dots, m\}v$. The necessary and sufficient conditions only
depending on $b,c,m$ are given for the $T(A,\mathcal{D})$ to be connected.
Moreover, we also consider the case that ${\mathcal D}$ is non-consecutively
collinear.
