Spring constant from slope of length-load graph Steps:

• Identify the graph as length (y-axis) vs. load/force (x-axis); the line's slope is Δlength/Δforce = 1/k.
• Read the slope from the graph: rise over run gives approximately 0.125 m/N.
• Calculate k = 1 / slope = 1 / 0.125 = 8 N/m.
• Confirm units: N/m, matching Hooke's law F = kx where x is extension (Δlength).

Why D is correct:

• k = 8 N m^{-1} matches the reciprocal of the graph's slope, per Hooke's law definition.

Why the others are wrong:

• A: 0.05 N m^{-1} is the slope itself, not its reciprocal.
• B: 0.13 N m^{-1} approximates the slope but ignores inversion for k.
• C: 2 N m^{-1} miscalculates reciprocal (e.g., 1/0.5 error).

Final answer: D