The table below shows three values of $x$ and their corresponding values of $g(x)$, where $g(x)=f(x)+h(x)$, $f(x)$ is a linear function, and $h(x)=-2x+1$.

x	g(x)
2	-5
5	1
8	7

What is the $x$-intercept of the graph of $y=g(x)$ in the $xy$-plane?