Why is the income effect zero for quasilinear utility functions?
From the formula for $x_M$, we see it has no dependence on income $m$. So $$\frac{\partial x_M}{\partial m} =0$$ Thus, the Slutsky equation 

$$\frac{\partial x_M}{\partial p_x} = \frac{\partial x_H}{\partial p_x} +-\frac{\partial x_M}{\partial m}x_M$$

implies 

$$\frac{\partial x_M}{\partial p_x} = \frac{\partial x_H}{\partial p_x} +(0)x_M $$
$$\frac{\partial x_M}{\partial p_x} = \frac{\partial x_H}{\partial p_x}  $$
Hence, and since $-\frac{\partial x_M}{\partial m}x_M$ is the income effect, this implies the income effect is zero and all the change is due to the substitution effect.