FTCE Professional Education Practice Exam

What would the graph indicate if the solution to an inequality is y less than or equal to a number?

1. Diagonal line

2. Vertical line

3. Horizontal line

4. Curved line

The correct answer is: Horizontal line

The correct answer is indeed the choice indicating a horizontal line. When dealing with the inequality y ≤ k, where k is a specific number, the graph represents all points where the y-coordinate is less than or equal to k. This results in a horizontal line drawn at the y-value equal to k, extending infinitely to the left and right. The region below this line would be shaded to represent all the solutions that satisfy the inequality, indicating that any value of y below this line is included in the solution set, as well as the line itself. The other options represent different types of lines or slopes. A diagonal line would suggest a relationship where y changes with respect to x, which does not apply here. A vertical line would imply that x is limited to a specific value regardless of y's value, contradicting the form of the inequality. A curved line could suggest a more complex relationship, typically seen in quadratic or other non-linear functions, which is not relevant for a simple linear inequality like y ≤ k. Thus, the choice of a horizontal line is the most accurate and appropriate representation for this inequality.