Final answer:
The slope of a line that makes a 60° angle with the positive direction of the X-axis is √3.
Step-by-step explanation:
The slope of a line in a coordinate plane is a measure of how steep the line is, and it can be calculated using the tangent of the angle the line makes with the positive direction of the x-axis. In this case, the line makes a 60° angle with the positive x-axis. The tangent of 60° is √3, which means that the slope of the line is √3.
Therefore, the correct answer to the student's question is C. √3. This demonstrates how understanding the angle's tangent enables the calculation of the line's slope, providing a definitive answer within the context of coordinate geometry.