determine the ratio in which the line 3x+y-9=0 divides the segment joining the points (1,3) and (2,7).

Let the point be (x,y) , and the ratio it divides (1,3) and (2,7) be k:1

By section formula , x = (2k+1)/(k+1)  ,  y = (7k+3)/(k+1)

his point also lies on the given line so it would satisfy the equation 3x+y-9=0

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

k = 3/4

ratio = 3:4