Line $h$ has the equation $y=mx+b$, where $m$ and $b$ are constants. Line $k$ is the result of translating line $h$ up $c$ units, where $c$ is a positive constant. Which of the following statements must be true?

I. The slope of line $k$ is $m$.
II. The $y$-intercept of line $k$ is $b+c$.
III. The $x$-intercept of line $k$ is $x_h-\frac{c}{m}$, where $x_h$ is the $x$-intercept of line $h$.