Hooke's Law

Hooke's law is a proportionality, not a value. It says how the force a spring exerts changes when you pull it further, and the constant of proportionality is a property of that particular spring.

That is the form the AP Physics 1 equation sheet prints, and AP Physics 1 essential knowledge 2.8.A.2 names it as Hooke's law. The setup is 2.8.A.1: an ideal spring has negligible mass and exerts a force that is proportional to the change in its length as measured from its relaxed length.

Read the minus sign as a direction, not a negative number. It records that the force opposes the stretch. 2.8.A.3 says the force exerted on an object by a spring is always directed toward the equilibrium position of the object and spring system, so a spring pulled right pushes left, and a spring compressed left pushes right. The magnitude is $k \lvert \Delta x \rvert$ and is never negative.

$\Delta x$ is measured from the relaxed length, the length the spring sits at with nothing attached, not from where a hanging mass happens to rest. Hang a block on a vertical spring and it settles at a new position where the spring is already stretched, and that stretch counts.

Two things Hooke's law is not. It is not the spring constant, which is the single number $k$ that this relationship contains. And it is not the definition of simple harmonic motion, which needs the more general condition in restoring force. The procedure for using it in an oscillation problem is in simple harmonic motion.