suppose the line 2x+3y-5=0 divides the line segment a(8,-9) and b(2,7) in the ratio k:1 at point c.

then the coordinates of the point c are

(2k+8/k+1,7k-9/k+1)

but c lies on 2x+3y-5=0

therefore: 2(2k+8/k+1)+3(7k-9/k+1)-5=0

=4k+16+21k -27-5=0

=25k-16=0

=25k=16

=k=16/25 i hope this answer is correct:)