Simple question on Laplace's Equation (electrostatics)

[Abdul.119]

Homework Statement

Consider solutions to the One Dimensional Laplace's Equation in Cartesian Coordinates

Let the range of x be from x1 to x2 (x1 > x2) and the boundary conditions are V[x1] = V1 and V[x2] = V2

Find the equation for V[x]

Homework Equations

V[x] = 1/2 (V(x+a)+V(x-a))
V[x] = mx + b

The Attempt at a Solution

I don't understand what equation I'm asked for.. from what I know the slope m is the difference in V over the difference in x, and the b is V2*x1 - V1x2 / x1-x2. Do I just apply that here? what about the equation V[x] = 1/2 (V(x+a)+V(x-a)) ?

 

[Simon Bridge]

You are supposed to find V(x) using Laplaces equation $\nabla^2V=0$
Do so ... start by writing down the 1D Laplaces equ as an appropriate boundary value problem, then solve the equation normally.