The graph of the function $f(x)=2x-3$ is a line in the $xy$-plane. If a new function $g(x)$ is defined such that its graph is parallel to the graph of $f(x)$ but has a $y$-intercept that is $5$ units greater than the $y$-intercept of $f(x)$, which of the following defines $g(x)$?