Robert initially bakes 6 pies with the sugar he has. For every additional cup of sugar he buys, he can bake 1 more pie. Therefore, the total number of pies he can bake, \( y \), depends on the number of cups of sugar he buys, \( x \), can be expressed with the following equation:
\[ y = 6 + x \]
Here, \( 6 \) represents the number of pies he can bake with the sugar he initially has, and \( x \) represents the additional pies he can bake by purchasing \( x \) extra cups of sugar.