The MRS$_{xy}$ is defined as $\left(-\frac{dy}{dx}\right)$ and Nicholson/Snyder (NS) writes it as the amount of $x$ we can trade for $y$ while remaining equally well off.
However, the analytical definition however tells something different, that in a sufficiently close neighbourhood of $(x,y)$, $y\mp \left(-\frac{dy}{dx}\right) = m(x \pm 1) + c$, which can be interpreted as: the amount of $y$ we need to give or get (trade off) for a unit of $x$ (while remaining equally well off).
The two statements sound contradictory, the first one says we need to exchange $x$ at the MRS for every unit of $x$ and the second one says quite the opposite, that we substitute $x$ at the MRS for every unit of $y$.
Is it a mistake in the book by NS?