Answer:
no universal test point
Step-by-step explanation:
You want to know if there is or is not a universal test point that can be used for testing the shading for a linear inequality.
The purpose of a test point for the graph of an inequality is to determine whether the shaded area includes the test point or not. A single inequality will divide the universal set into two parts: one part that is the solution set, and one part that is not the solution set.
A point that is well inside the solution set (or not-a-solution set) will tell you which side of the boundary is shaded. Any point that always meets that requirement could be considered a universal test point.
The boundary point(s) between these sets may or may not be shaded, but its(their) shading, or lack of it, will not tell you which half of the universal set is the solution set. That is, any point that falls on the boundary of the solution set is not a suitable test point.
The boundary can be anywhere, so there is no single universal test point.
__
Additional comment
A set of three non-collinear points can be considered to be a universal test set. Together, they can tell you which part of the universal set is the solution set. At most, the boundary line can pass through two of them, so the third can tell you which half of the universe it lies in.
