Suppose we have utility:
$$U(x,y)=x^{0.5}y^{0.5}$$
Then Marshallian Demand for good $x$ is:
$$x(p_{x},p_{y},I)=\frac{0.5I}{p_{x}}$$
And Hicksian Demand for good $x$ is:
$$x^{c}(p_{x},p_{y},U)=p_{x}^{-0.5}p_{y}^{0.5}U$$
If $p_{x}=1$, $p_{y}=4$, $I=8$ and $U=2$:
Marshallian Demand for $x$ is 4 and Hicksian Demand for $x$ is 4.
Supposing that the price of good $x$ rises to $p_{x}=4$, how can the Slutsky equation show us the change due to substitution effect and income effect?
Substitution effect: $\frac{\partial x^c}{\partial p_{x}}=-0.25p_{x}^{-2}I$ according to the Slutsky equation. If we plug in $p_{x}=4$, the result is -0.125. How is that meaningful in any way? The Hicksian Demand should drop from 4 to 2 after this price increase but I don't see how the Slutsky equation shows us that.