It depends what graph you have drawn.
Why would it not go through the origin?
Hooks'e Law applies when the extension is directly proportional to the tension.
If that's what happens to the spring, then Hooke's Law applies.
If you apply add 0.1kg, for example and it stretches 10cm, and you apply another 0.1kg and it stretches another 10cm then that is obeying Hooke's Law.