find the ratio in which the line 2x+3y-5=0.so the line divides the line segment divide the points a(8, -9) and (2,-1) also find the coordinates of the point of division

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:)