The reaction of silver nitrate with copper is a substitution reaction. We have copper in its free state, Cu, and we have silver nitrate which has the formula AgNO3. The copper replaces the silver obtaining the following reaction:
[tex]2AgNO_{3(aq)}+Cu_{(s)}\rightarrow Cu(NO_3)_{2(aq)}+2Ag_{(s)}[/tex]The products obtained are copper nitrate and silver.
The word equation will be:
[tex]SilverNitrate+Copper\rightarrow Copper(II)Nitrate+Silver[/tex]