The function $f$ is defined by $f(x)=(x+a)(x+b)$, where $a$ and $b$ are positive integer constants. The functions $g$ and $h$ are equivalent to function $f$, where $k$ and $m$ are constants. Which of the following equations displays the $y$-coordinate of the $y$-intercept of the graph of $y=f(x)$ in the $xy$-plane as a constant or coefficient?

I. $g(x)=x^2+(a+b)x+k$
II. $h(x)=x(x+a+b)+m$