Spring constant equals slope of force vs. displacement graph

Steps:

• Recall Hooke's law: F = kx, so k = slope of F vs. x graph.
• Examine graphs 1–4 for their slopes (steepest to shallowest indicates largest to smallest k).
• Rank by decreasing slope: graph 4 (steepest), then 2, then 3, then 1 (shallowest).
• Match ranking to choices for decreasing k order.

Why C is correct:

• Option C (4-2-3-1) orders graphs from highest to lowest slope, matching decreasing k per Hooke's law.

Why the others are wrong:

• A starts with 2 (not steepest), skips highest k.
• B starts with 3 (medium slope), not highest k.
• D starts with 1 (shallowest), reverses decreasing order.

Final answer: C