If we have a spring with natural length $l$, modulus of elasticity $\lambda$ and it has a weight of $m_1g$ attached to it, then its extension, $x_1$, is $$\frac{m_1gl}{\lambda}$$ If we add on another mass with weight $m_2g$ then we find the change in extension, $x_2$, is $$\frac{m_2gl}{\lambda}$$ after some manipulation.
Hooke's law states that the tension in a spring, $T$, is equal to the spring constant, $k$, multiplied by the extension of the spring, $x$:
$$T=kx=\frac{\lambda x}{l}~~(\text{as the spring constant is equal to $\frac{\lambda }{l}$})$$
Therefore, is it correct to state Hooke's law somewhat differently:
$$\Delta T=\frac{\lambda\Delta x}{l}$$ where $\Delta T$ is the change in tension in the spring.
Mathematically this seems sound; I'd just like to verify this is true.
EDIT:
There seems to be some confusion about the measurements and terms that I have used. To clarify:
The spring constant, $k$, is equal to $\lambda/l$; so my question is equivalently: is the following variation of Hooke's Law correct?
$$\Delta T=k\Delta x$$ where $\Delta T$ is the change in tension in the spring and $\Delta x$ is the change in extension.