Final answer:
Dotted lines or open circles on a graph represent non-inclusive inequalities, symbolized by '>' for greater than and '<' for less than. These indicate that the endpoint is not part of the solution set. Solid lines or closed circles represent inclusive inequalities using '≥' and '≤'.
Step-by-step explanation:
In the context of graphing inequalities on a number line or a coordinate plane, dotted lines or open circles represent inequalities that are not inclusive of the boundary point, which means the value at that point is not part of the solution set. The symbols that represent these types of inequalities are '>' for greater than and '<' for less than. For example, if we have x > 3, this would be represented by an open circle at the 3 on the number line with a line extending to the right to indicate all numbers greater than 3 are included in the solution set. If we have x < 2, then we would have an open circle at 2 and a line extending to the left.
When equal to is included in the inequality, as with the symbols '≥' (greater than or equal to) and '≤' (less than or equal to), a solid line or closed circle is used to indicate that the endpoints are part of the solution set.