In graphing, what indicates that a value is included in a number line representation?

A closed circle on a number line indicates that a value is included in the representation. This means that the endpoint of the interval is part of the set being represented. For instance, if you were graphing the inequality x ≤ 3, you would use a closed circle at 3 to show that 3 is included in the solution set.

In contrast, an open circle would indicate that the value is not included in the solution, which would be used for inequalities like x < 3. The solid line typically signifies a continuous range of values connecting the points, while a dashed line is often used to show that the line does not include the endpoint values, reinforcing the use of open circles. Understanding how to use closed circles correctly is essential for accurately representing intervals and inequalities on a number line.