We have the following 4 equations to solve for the 4 unknowns m, b, q', and p':
Performing the integration in equation (4) gives
Substituting equation (2) into equation (5) yields
and solving for q' yields
Then by equation (2)
Substituting equation (1) into equation (3) yields
and solving for m, using q', gives
Substituting the m, q', and p' we have found into equation (1) gives
So the final answers are that the equilibrium point is at
and that the equation for the linear demand curve is
