Hooke's Law Defines the Slope as Spring Constant

Steps:

• Hooke's law states that force (F) is proportional to extension (x), given by F = kx, where k is the spring constant.
• Plotting F (y-axis) against x (x-axis) yields a straight line through the origin for elastic behavior.
• The gradient (slope) of this line is rise over run, or ΔF/Δx, which equals k.
• Thus, the gradient directly represents the spring constant k.

Why B is correct:

• Hooke's law formula F = kx shows the slope of the F vs. x graph is k, the spring constant measuring stiffness.

Why the others are wrong:

• A: Elastic limit is the maximum extension before permanent deformation, not a graph slope.
• C: Stress is force per unit cross-sectional area, unrelated to the F vs. extension slope.
• D: Young's modulus is stress divided by strain, requiring material properties beyond this graph.

Final answer: B