Graph #1 is a parabola. Graph #2 is a hyperbola.

a. Only graph 1 may possibly represent Hooke's law
b. Only graph 2 may possibly represent Hooke's law
c. neither

To determine whether either graph can represent Hooke's law, we need to understand what Hooke's law represents and how it is mathematically expressed.

Hooke's law states that the force needed to extend or compress a spring by a distance is directly proportional to that distance. Mathematically, Hooke's law can be expressed as F = kx, where F represents the force, k is the spring constant (a measure of the stiffness of the spring), and x represents the displacement of the spring from its equilibrium position.

Now let's analyze the given graphs:

1. Parabola: A parabola is the graph of a quadratic equation in the form of y = ax^2 + bx + c. The equation of a parabola does not match the form of Hooke's law (F = kx). Therefore, it is unlikely that graph 1 represents Hooke's law.

2. Hyperbola: A hyperbola is a curved shape that has two separate branches that extend indefinitely. The equation of a hyperbola is generally represented by the equation (x - h)^2 / a^2 - (y - k)^2 / b^2 = 1. Similar to the parabola, the equation of a hyperbola does not match the form of Hooke's law (F = kx). Hence, it is also unlikely that graph 2 represents Hooke's law.

Therefore, the answer is: c) neither graph 1 nor graph 2 may possibly represent Hooke's law.