A90 kg architect is standing 2 meters from the center of a scaffold up by a rope on both sides. the scaffold is 6m long and has a mass of 200kg. what is the tension on each rope

We can solve the problem by requiring the equilibrium of the forces and the equilibrium of torques.

1) Equilibrium of forces:

where
is the weight of the person
is the weight of the scaffold
Re-arranging, we can write the equation as
(1)

2) Equilibrium of torques:

where 3 m and 2 m are the distances of the forces from the center of mass of the scaffold.
Using and replacing T1 with (1), we find

from which we find


And then, substituting T2 into (1), we find

Alinear relationship would look like a straight line on the graph. it could have a positive negative or 0 slope. so it could be a line potentially going in any direction but it must be perfectly straight.