Knowing that the gradient in a stress strain graph is equal to the modulus of elasticity?

which can also be termed as Young's Modulus but how could I define this term?Knowing that the gradient in a stress strain graph is equal to the modulus of elasticity?
The usual definition of Young's modulus is stress/strain, where





stress= force/unit area, and





strain = extension/original length.





If the stress-strain graph is linear, (Hook's Law obeyed, elastic deformation) this definition is the same thing as the slope of the graphKnowing that the gradient in a stress strain graph is equal to the modulus of elasticity?
You could define it as the slope of the linear portion of the graph. That is, in fact, what it is defined as.





Its physical meaning is the material's resistance to changing in length when a uniaxial stress is applied.
the worded definition will be the same as for stiffness -- a material which is resistant to change in shape and form. it is indeed the young modulus. the mathematical definition would be YM= stress/strain