Spring constant from slope of length-force graph Steps:

• Read the natural length L0 from the graph where force F=0.
• Select two points on the linear portion: note changes in length ΔL and force ΔF.
• Calculate gradient = ΔL / ΔF (in m/N).
• Compute k = 1 / gradient (in N/m) using Hooke's law F = kx, where x=ΔL.

Why D is correct:

• Hooke's law states F = k ΔL, so for L vs. F graph, slope = ΔL/ΔF = 1/k; graph yields k=6 N/m.

Why the others are wrong:

• A: Equals the graph's slope directly, ignoring reciprocal.
• B: Possible arithmetic error in ΔL or ΔF calculation.
• C: Misapplies formula by using ΔF/ΔL instead of reciprocal.

Final answer: D