The graph of the function $y = k \cdot 3 ^ { x }$ ($0 < k < 1$) meets the graphs of the two functions $y = 3 ^ { - x }$ and $y = - 4 \cdot 3 ^ { x } + 8$ at points P and Q, respectively. When the ratio of the $x$-coordinates of points P and Q is $1 : 2$, find the value of $35k$. [4 points]