#### Answer

$$x =3+8t, \quad y= 1-3t.$$

#### Work Step by Step

First, we find the slope $m=\frac{4-1}{-5-3}=\frac{3}{-8}$.
Now, we have $m=\frac{s}{r}=-\frac{3}{8}$ so take $r=8$ and $s=-3$. Then, the parametric equations are
$$x=a+rt=3+8t, \quad y= b+st=1-3t.$$
That is,
$$c(t)=(x(t),y(t))=(3+8t,1-3t).$$