FTCE Professional Education Practice Exam

Which of the following is a characteristic of a vertical line in graphing inequalities?

1. It represents all values of y

2. It represents constant x values

3. It slopes downwards

4. It does not intersect the y-axis

The correct answer is: It represents constant x values

A vertical line in graphing inequalities is defined as having a constant x-value. This means that no matter what value y takes on, x remains the same for all points along that vertical line. For example, the equation x = 3 represents a vertical line where x is always 3, while y can be any real number. In the context of graphing inequalities, vertical lines are essential for illustrating constraints based on fixed x-values. For instance, an inequality like x ≥ 3 would show all points to the right of the line x = 3, which includes every possible y-value for that x-value. Other options like representing all values of y or having a downward slope do not accurately describe the properties of vertical lines. A vertical line does indeed intersect the y-axis, as it runs perpendicular to the x-axis. Therefore, the defining characteristic of vertical lines in graphing inequalities is that they represent constant x values.