Suppose parametric equations for the line segment between $(0, 2)$ and $(0, 6)$ have the form: $$\begin{array}{r@{\,}c@{\,}l} x & = & a + bt \cr y & = & c + dt \end{array}$$ If the parametric curve starts at $(0, 2)$ when $t=0$ and ends at $(0, 6)$ at $t=1$, then find $a$, $b$, $c$, and $d$.
$a =$ ,
$b =$ ,
$c =$ ,
$d =$ .