- The mechanical property quantified by the slope of the linear portion of a stress-strain curve is the Young's modulus (Elastic modulus).
- This portion represents the elastic region of the material, where deformation is reversible, meaning the material will return to its original shape when the applied stress is removed.

- Young's modulus is a measure of the stiffness of a material, indicating how much it will deform under a given load.
- It is defined as the ratio of stress (force per unit area) to strain (deformation relative to original length) in this elastic region.
- A steeper slope corresponds to a higher Young's modulus, meaning the material is more rigid.

To clarify the other options:
- Poisson's ratio is the ratio of lateral strain to axial strain and describes the material's volumetric changes when stretched.
- Yield strength is the stress at which permanent (plastic) deformation begins.
- Ductility refers to the extent to which a material can undergo plastic deformation before fracture.

Understanding these distinctions is crucial for interpreting the stress-strain curve accurately and selecting materials for specific mechanical applications.

Reference: Materials Science and Engineering: An Introduction, Volume 1, Chapter 4, pp. 120-130