To solve this problem, we need to find the coordinates of the point where the line x + y = 4 intersects the line joining the points (-1, 1) and (5, 7).

Step 1: Find the equation of the line joining the points (-1, 1) and (5, 7).
The slope of the line can be found using the formula:
m = (y2 - y1) / (x2 - x1)
m = (7 - 1) / (5 - (-1))
m = 6 / 6
m = 1

Using the point-slope form of a linear equation, we can write the equation of the line as:
y - y1 = m(x - x1)
y - 1 = 1(x - (-1))
y - 1 = x + 1
y = x + 2

Step 2: Find the coordinates of the point of intersection.
To find the point of intersection, we need to solve the system of equations:
x + y = 4
y = x + 2

Substituting the value of y from the second equation into the first equation, we get:
x + (x + 2) = 4
2x + 2 = 4
2x = 2
x = 1

Substituting the value of x into the second equation, we get:
y = 1 + 2
y = 3

Therefore, the point of intersection is (1, 3).

Step 3: Find the ratio in which the line divides the line segment.
To find the ratio in which the line divides the line segment, we can use the distance formula. Let's call the point of intersection P and the two given points A and B.

The distance between A and P can be calculated as:
AP = sqrt((x2 - x1)^2 + (y2 - y1)^2)
AP = sqrt((1 - (-1))^2 + (3 - 1)^2)
AP = sqrt(2^2 + 2^2)
AP = sqrt(8)
AP = 2sqrt(2)

The distance between B and P can be calculated as:
BP = sqrt((x2 - x1)^2 + (y2 - y1)^2)
BP = sqrt((5 - 1)^2 + (7 - 3)^2)
BP = sqrt(4^2 + 4^2)
BP = sqrt(32)
BP = 4sqrt(2)

Therefore, the ratio in which the line divides the line segment is:
AP : BP = 2sqrt(2) : 4sqrt(2) = 1 : 2

Hence, the correct answer is option B) 1 : 2.