Find the parametric curver from points (2,1) and (5,4)

Question

I already found $x=2+3t$ and $y=1+3t$ but I don't know how to get the whole equation of $r(t)=$? and what the boundaries are $?<t<?$

Answer 1

You're done. Or maybe you want to write $$ r(t) = (2 + 3t, 1 + 3t), 0 \le t \le 1, $$ to make it a little more complete.