The table shows three values of $x$ and their corresponding values of $g(x)$, where $g(x)=\frac{f(x)}{x-4}$ and $f$ is a linear function. What is the $y$-intercept of the graph of $y=f(x)$ in the $xy$-plane?

x	g(x)
6	5
9	8
12	11