Is this graph valid for certain cases or always true? If invalid, when is it valid?
The shape of the curve and the word "series" on the curve indicate that the curve is for a motor with the armature and field wired in series with each other. Permanent magnet motors, motors with the armature and field connected in parallel (shunt), and motor with a separate power supply for the armature and field, have curves that are more like straight lines as shown below. The curved red lines are for a series motor and the straight green lines are for a permanent magnet motor. The dotted lines show the effect of voltage reduction.
The location location of the operating point is the point where the load line crosses the motor curve. The load line is the characteristic of the load that shows how much torque is required to drive it at a given speed. The applied voltage adjusts the speed by moving the motor curve and the operating point. The shape of the curve as determined by the motor design, determines how much influence the applied voltage and the motor current (torque) each have on the operating speed.
Note that motors normally operate on the small portion of the curve at or below the rated current (100%). In that range, the load has much less influence on the speed than does voltage, for motors with a permanent magnet, shunt or separately powered field.
The load line is the steady-state speed vs. torque characteristic of the load driven by the motor. The % current axis for the speed vs current motor curves can be considered to represent % torque for the purpose of illustration. The equation for the load line is a summation of friction, fluid drag, gravitational forces and any other forces that oppose the rotation of the drive shaft.
For most loads, torque increases as speed increases. For centrifugal pumps and fans, load increases in proportion to the square of the relative speed increase. For most other loads, torque is relatively constant to slightly increasing with speed. Torque decreases with speed increase only when there is an active control mechanism that reduces the torque, such as increasing the speed and reducing the force on the bit when drilling with a smaller bit. The load line is normally determined only by the characteristics of the load and completely independent from the motor characteristics.