Let x-axis divides the line segment joining (–4, –6) and (–1, 7) at the point P in the ratio 1 : k.
Now, coordinates of point of division P are
x coordinate = (-1 - 4k) / (k + 1)
y coordinate = (7 - 6k) / (k + 1)
Since P lies on x-axis, therefore y coordinate = 0
(7 - 6k) / (k + 1) = 0
7 - 6k = 0
k = 7/6
Hence, the ratio is 1:7/6 = 6:7
x=(-k-4)/k+1 =((-6/7 -4))/(6/7 +1) =-34/13
x=-34/13