vector representation of line i know that  vector representation of curve that starts at $r_0$  and ends at $r_1$ is given by
$$r(t)=(1-t) r_0+t r_1\text{ where }0<t<1$$
so suppose  $r_0=(-5,3)$  and $r_1=(0,2)$, now  we should have 
$r(t)=(1-t) (-5,3)+t (0,2)$
if we  add separately we get $r(t)=(5 t-5,3-3 t)+(0,2 t)$
so finally it should be  $x=5 t-5$ and  $y=3-t$,but in answers it is written that $y=5 t-3$where i made mistake? thanks in advance

It doesn't look like you have any mistake in your math. However, the most likely thing that I can see being wrong is that you copied the problem out wrong, and $r_0$ was supposed to be $(-5, -3)$, not $(-5, 3)$, as that would give the answer that you say is given. Either that, or the answer is wrong.
