Which of the following equations represents a horizontal line?

A horizontal line on a graph is defined by a constant value of y while the x-coordinate can take any value. In this case, the equation y = k represents a horizontal line because, regardless of the value of x, the y-coordinate remains constant at k.

For any value of k, the points on this line would share the same y-coordinate, leading to a straight line that runs parallel to the x-axis. This is a clear characteristic of horizontal lines.

In contrast, the other equations do not represent horizontal lines. The equation x = k describes a vertical line where the x-coordinate is fixed, while the equation y = mx + c is a linear equation that results in a line with a slope (m), which is not horizontal unless m is zero. The equation y = x² represents a parabolic curve, not a line. Thus, y = k is indeed the defining equation for a horizontal line.