Let’s consider the point P($2$, y) divide the line segment joining the points A$(-2,2)$ and B$(3,7)$ in the ratio k: 1

Now, the coordinates of P are given by

$\left[ \frac{3k+(-2)\times 1}{k+1},\frac{7k+2\times 1}{k+1} \right]$

$=\left[ \frac{3k-2}{k+1},\frac{7k+2}{k+1} \right]$

And, given the coordinates of P are ($2$, y)

So,

$2=(3k–2)/(k+1)$ and y$=(7k+2)/(k+1)$

Now Solving for k we get,

$2(k+1)=(3k–2)$

$2k+2=3k–2$

$k=4$

By Using k to find y, we have

y $=(7(4)+2)/(4+1)$

$=(28+2)/5$

$=30/5$

y $=6$

Therefore, the ratio id $4:1$ and y $= 6$