Introduction:
To find the ratio in which the line x+y=4 divides the line segment joining the points (1,-1) and (5,7), we will use the concept of Section Formula. The Section Formula helps us determine the coordinates of a point that divides a line segment into two parts in a given ratio.

Given Information:
- Line equation: x+y=4
- Points: A(1,-1), B(5,7)

Step 1: Finding the coordinates of the dividing point:
Let the dividing point be P(x, y) that lies on the line x+y=4. We need to find the coordinates of P.

Step 2: Determining the ratio:
We are given that the line x+y=4 divides the line segment AB in a certain ratio. Let the ratio be k:1, where k is a positive constant.

Step 3: Applying the Section Formula:
Using the Section Formula, we can find the coordinates of P as:
x = (k * x2 + x1) / (k+1)
y = (k * y2 + y1) / (k+1)

Step 4: Substituting the known values:
Substituting the values of A(1,-1), B(5,7), and the equation x+y=4 into the Section Formula, we get:

x = (k * 5 + 1) / (k+1)
y = (k * 7 - 1) / (k+1)

Step 5: Solving the equations:
To find the value of k, we need to solve the equation x+y=4 simultaneously with the Section Formula equations. This will give us the value of k.

Step 6: Calculating the ratio:
Once we obtain the value of k, we can calculate the ratio k:1. The value of k will determine how the line divides the line segment AB.

Conclusion:
By applying the Section Formula and solving the equations, we can find the ratio in which the line x+y=4 divides the line segment joining the points (1,-1) and (5,7). The ratio will depend on the value of k, which is obtained by solving the equations.