Solution:

Consider how line 2x + y – 4 = 0 divides line AB in a k:1 ratio joined by the two points A(2, -2) and B(3, 7).

The following are the coordinates of the point of division:

x = (2 + 3k)/(k + 1) and y = (-2 + 7k)/(k + 1)

Substitute the values of x and y in the given equation, i.e. 2x + y – 4 = 0, we have

2{(2 + 3k)/(k + 1)} + {(-2 + 7k)/(k + 1)} – 4 = 0

(4 + 6k)/(k + 1) + (-2 + 7k)/(k + 1) = 4

4 + 6k – 2 + 7k = 4(k+1)

-2 + 9k = 0

Or k = 2/9

As a result, the ratio is 2: 9.