Final answer:
Any region of the xy-plane satisfies the conditions for the existence and uniqueness of a solution for the differential equation dy/dx = xy, passing through any point (x₀, y₀).
Step-by-step explanation:
To determine a region of the xy-plane for which the differential equation dy/dx = xy would have a unique solution whose graph passes through a point (x₀, y₀), we need to consider the existence and uniqueness theorem for first-order differential equations.
According to this theorem, a differential equation of the form dy/dx = f(x, y) has a unique solution passing through a point (x₀, y₀) if the function f(x, y) and its partial derivative with respect to y are continuous in a region around (x₀, y₀).
Considering our equation dy/dx = xy, both f(x, y) = xy and its partial derivative with respect to y, which is x, are continuous everywhere on the xy-plane. Thus, for this equation, any region of the xy-plane satisfies the conditions for existence and uniqueness of a solution passing through any point (x₀, y₀) in that region.