A G-protein coupled acetylcholine receptor signaling pathway that contributes to a decrease in frequency or rate of heart contraction through activation of the IKACh potassium channel. Binding of acetylcholine to a G-protein coupled acetylcholine receptor (muscarinic receptor) on the surface of the signal-receiving cell results in liberation of the G-beta/gamma complex from the alpha subunit. The G-beta/gamma complex binds directly to the inward-rectifying potassium channel IKACh. Once the ion channel is activated, potassium ions (K+) flow out of the cell and cause it to hyperpolarize. In its hyperpolarized state, action potentials cannot be fired as quickly as possible, which slows the heart rate.