If an object is at rest, then the time (X-axis) versus distance (Y-axis) graph-

In a distance-time graph, time is typically plotted on the horizontal X-axis while distance is plotted on the vertical Y-axis. The slope of the line on this graph represents the speed or velocity of the object. When an object is at rest, its position or distance from a reference point does not change as time progresses. Consequently, the change in distance is zero, leading to a slope of zero. This state of rest is represented graphically by a horizontal line that runs parallel to the time axis. Unlike a sloping line which indicates constant speed, or a vertical line which would imply infinite speed (physically impossible for a single object), a horizontal line confirms the object remains stationary at a constant distance over the elapsed time.

Sources

1. [1] Microeconomics (NCERT class XII 2025 ed.) > Chapter 2: Theory of Consumer Behaviour > EXAMPLE 2 > p. 22