The pressure depends on the force being applied to the walls of the vessel. It goes up with temperature because the molecules have more energy. Remember the ideal gas law:
p = (nR/V)T
Above the indicated temperature, everything has been boiled, hence mass (and therefore n) is constant. The vessel has constant volume, so pressure varies linearly with temperature.
Why isnt the pressure on the walls by the particles ( which is constant shown by graph to be constant after T) the same as pressure of the particles dictated by ideal gas equation? I know it should increase but that contradicts the graph data isnt it? Increased pressure of the vapour should increase pressure on the walls why is the graph linear after time t?