Young's modulus equals the slope of the stress-strain graph

Steps:

• Young's modulus $E$ is defined as stress divided by strain: $E = \frac{\sigma}{\epsilon}$.
• Stress $\sigma = \frac{F}{A}$ (force over cross-sectional area); strain $\epsilon = \frac{\Delta L}{L_0}$ (extension over original length).
• Plotting stress (y-axis) vs. strain (x-axis) gives a straight line where slope = $\frac{\Delta \sigma}{\Delta \epsilon} = E$.
• Other graphs involve force and extension directly, which depend on wire dimensions, not just material properties.

Why C is correct:

• By definition, $E = \frac{\text{stress}}{\text{strain}}$, so the gradient of stress vs. strain is exactly $E$.

Why the others are wrong:

• A: Slope is $\frac{\Delta x}{F} = \frac{L_0}{A E}$, inversely related to .

Final answer: C