Here's why:

* Homogeneous: The silver nitrate dissolves completely in the water, creating a uniform composition throughout the mixture. You can't see individual particles of silver nitrate.

* Solution: A solution is a type of homogeneous mixture where one substance (the solute, in this case, silver nitrate) dissolves evenly into another substance (the solvent, in this case, water).

Therefore, silver nitrate in water is a homogeneous mixture, specifically a solution.