Here's how to write the net ionic equation for the reaction of aqueous lead(II) nitrate with potassium sulfate:

1. Write the balanced molecular equation:

Pb(NO₃)₂(aq) + K₂SO₄(aq) → PbSO₄(s) + 2KNO₃(aq)

2. Write the complete ionic equation:

This involves breaking down all soluble ionic compounds into their respective ions:

Pb²⁺(aq) + 2NO₃⁻(aq) + 2K⁺(aq) + SO₄²⁻(aq) → PbSO₄(s) + 2K⁺(aq) + 2NO₃⁻(aq)

3. Identify spectator ions:

Spectator ions are those that appear on both sides of the equation unchanged. In this case, K⁺(aq) and NO₃⁻(aq) are spectator ions.

4. Write the net ionic equation:

This involves removing the spectator ions:

Pb²⁺(aq) + SO₄²⁻(aq) → PbSO₄(s)

Therefore, the net ionic equation for the reaction is Pb²⁺(aq) + SO₄²⁻(aq) → PbSO₄(s).