Final answer:
Slow-wave sleep begins in Stage 3, characterized by delta waves, which show a low frequency and high amplitude.
Step-by-step explanation:
Slow-wave sleep begins in Stage 3 when an EEG shows about 20% of the brain waves are delta waves. Delta waves are characterized by their low frequency and high amplitude, distinct from the alpha and theta waves seen in the earlier stages of sleep. Specifically, stage 3 of Non-Rapid Eye Movement (NREM) sleep is often referred to as deep sleep or slow-wave sleep because it is dominated by these low frequency (less than 3 Hz), high amplitude delta waves. It is in this stage that vital functions like heart rate and respiration slow dramatically, and it is much more difficult to wake someone from sleep.