In which ratio and at which point does the $Y-$ axis divide the line segment joining $A(-2, 3)$ and $B(3, 0)$ from $A$?

(A) Suppose the $Y-$ axis intersects $\overline{AB}$ at point $P(0, y)$ and $P$ divides $\overline{AB}$ in the ratio $m:n$ from $A$.
Using the section formula for the $x-$coordinate:
$x = \frac{mx_2 + nx_1}{m+n}$
Since $P$ lies on the $Y-$ axis,its $x-$coordinate is $0$.
$0 = \frac{m(3) + n(-2)}{m+n}$
$0 = 3m - 2n$
$3m = 2n \implies \frac{m}{n} = \frac{2}{3}$
So,the ratio is $2:3$.
Now,find the $y-$coordinate of $P$ using the ratio $m=2$ and $n=3$:
$y = \frac{my_2 + ny_1}{m+n}$
$y = \frac{2(0) + 3(3)}{2+3} = \frac{9}{5}$
Thus,the point of division is $(0, 9/5)$ and the ratio is $2:3$.