In the $xy$ plane, the point $(a,b)$ lies on the line with the equation $y = x+c$ where $c$ is a constant. The point with coordinate $(3a,2b)$ lies on the line with equation $y=3x+c$. If $a \neq 0$. What is the value of $\frac{b}{a}$ ?

Question

$\begin{array}{1 1} (a)\; \frac{1}{8} \\ (b)\; -\frac{1}{8} \\ (c)\;8\\(d)\;-8 \end{array}$