hmmm interestin.........

Supose that the line divedes the line segment joining (-3,1) and ( 8,9) in the ratio k:1 in the point P(say).

So,

 using the section formula, we get,

the coordinates of P are

[(-3+8k)/k+1  ,(1+9k)/k+1]

But P must lie o the line x-y-2=0

So, the coordinates of P must satisfy the equation  x-y-2=0

So, substitute the coordinates of P in this equation  and you will get the value of  k.

That will give you the required ratio k:1