#### Answer

$$x= \frac{1}{3}+t, \quad y= \frac{1}{6}-t.$$

#### Work Step by Step

First, we find the slope $m=\frac{\frac{10}{6}-\frac{1}{6}}{-\frac{7}{6}-\frac{2}{6}}=\frac{9}{-9}=-1$.
Now, we have $m=\frac{s}{r}=-1$ so take $r=1$ and $s=-1$. Then, the parametric equations are
$$x=a+rt=\frac{1}{3}+t, \quad y= b+st=\frac{1}{6}-t.$$
That is,
$$c(t)=(x(t),y(t))=(\frac{1}{3}+t,\frac{1}{6}-t).$$