Let the given line divides the line segment joining the points in the ration k : 1 at C

So, by section formula,

Coordinate of C = {(2k + 1)/(k + 1), (7k + 3)/(k + 1)}

This point lies on the line 3x + y - 9 = 0

So, 3(2k + 1)/(k + 1) + (7k + 3)/(k + 1) - 9 = 0

=> 3(2k + 1) + (7k + 3) - 9(k + 1) = 0

=> 6k + 3 + 7k + 3 - 9k - 9 = 0

=> 4k - 3 = 0

=> 4k = 3

=> k = 3/4

So, the required ratios = 3/4 : 1

                               = 3 : 4