Add masses to a spring and watch it stretch. As long as you do not overload it, the extension is proportional to the force: that is Hooke's law.
Force
Extension
Spring constant
Hooke's law
Force = spring constant × extension (F = k × x). While the graph is a straight line through the origin, the spring is behaving elastically: double the force and you double the extension. Past the elastic limit the line bends over, the spring is permanently stretched and no longer springs back to its original length.
Check yourself
What does it mean when the force-extension graph is a straight line?
The extension is proportional to the force, so the spring obeys Hooke's law. Adding equal weights stretches it by equal amounts.
What is the elastic limit?
The point beyond which a spring is stretched so far that it no longer returns to its original length. On the graph the line stops being straight and curves.
A spring extends 4 cm when a force of 8 N is applied. What is its spring constant?
2 N/cm. The spring constant k = force ÷ extension = 8 ÷ 4 = 2 newtons per centimetre.