FTCE Professional Education Practice Exam

If an inequality results in x being greater than or equal to a number, what does the graph represent?

1. A horizontal line

2. A vertical line

3. A unique point

4. A diagonal line

The correct answer is: A vertical line

When an inequality results in x being greater than or equal to a specific number, the graph represents a vertical line at that number. This is because the inequality x ≥ a indicates that all values of x to the right of the vertical line (and including the line itself) satisfy the inequality. In this case, the vertical line is drawn at the point x = a, and the shaded region extends indefinitely to the right of this line, indicating all the values of x that meet the condition of being greater than or equal to a. The inclusion of "or equal to" means that the line itself is part of the solution set, which is why it is drawn as a solid line, rather than a dashed one which would indicate that values on the line are not included. Other options do not correctly represent the inequality involving x. For example, a horizontal line would imply that the y-value is being constrained, while a unique point or diagonal line would not accurately reflect the range of x-values that satisfy the inequality.