A line passing through two points \vec{r_0} and \vec{r_1} is simply
\vec{r}=(1-t)\vec{r_0}+t\vec{r_1}
You are given a point that you want the line through and you can figure out another arbitrary one right?
The definition of a rational function is any function that satisfies/can be expressed as
f(x)=\frac{P(x)}{Q(x)}
So when thinking whether (3) is rational or not, think about what happens if Q(x)=1 in this definition.