**Slope-Deflection Method**

The slope-deflection method is a structural analysis technique used to determine the displacements and moments in a beam or frame structure. It is based on the assumption that the deflection of a beam is proportional to the bending moment in the beam.

**Equation for Member AB**

To find the correct slope-deflection equation for member AB in the given beam, we need to consider the fixed end at A and the guided roller at B, as well as the applied loading of a UDL (Uniformly Distributed Load) of 20 kN/m over a length of 6 m.

**Step 1: Calculating the Fixed End Moment at A (MA)**

The fixed end moment at A (MA) can be calculated using the formula:

MA = (wL^2)/12

where:
w = UDL (Uniformly Distributed Load)
L = Length of the beam

Substituting the given values:
w = 20 kN/m
L = 6 m

MA = (20 * 6^2)/12
= (20 * 36)/12
= 60 kNm

Therefore, the fixed end moment at A is 60 kNm (taking anticlockwise moment as positive).

**Step 2: Applying the Slope-Deflection Method**

To apply the slope-deflection method, we need to consider the slope (θ) and the rotation (∆) at point B.

Let θB represent the slope at B, and ∆B represent the rotation at B.

**Step 3: Writing the Slope-Deflection Equation**

The slope-deflection equation for a member can be written as:

Mab = (EI/L) * (∆B - ∆A)

where:
Mab = Moment at B due to rotation at B (unknown)
EI = Flexural rigidity of the member
L = Length of the member
∆B = Rotation at B (unknown)
∆A = Rotation at A (known)

In this case, the slope-deflection equation for member AB can be written as:

Mab = (EI/6) * (∆B - 0)

Since the beam is fixed at A, the rotation at A (∆A) is zero.

Therefore, the correct slope-deflection equation for member AB is:

Mab = (EI/6) * ∆B

**Step 4: Substituting the Given Values**

The given answer choices are:
- Mab = 60 * (∆B / 6)
- Mab = -60 * (∆B / 6)

Substituting the given values into the slope-deflection equation:
Mab = (EI/6) * ∆B

Comparing this with the given answer choices, we can see that the correct equation is:
- Mab = 60 * (∆B / 6)

The negative sign in the second answer choice is incorrect because it violates the assumption of taking anticlockwise moment as positive.

Therefore, the correct slope-deflection equation for member AB is:
- Mab = 60 * (∆B / 6)