Gradient as a Rate of Change
Grade 5Gradient tells you the rate
Gradient isn't just a number — it has a meaning depending on what the axes represent. On a distance-time graph, the gradient of the line is the speed. A steeper line means a faster object.
On a speed-time graph, the gradient is acceleration — how quickly speed is changing. A flat line means constant speed (zero acceleration). A rising line means speeding up.
How to read gradient in context
The units of the gradient come directly from the axes. If the y-axis is distance in metres and the x-axis is time in seconds, the gradient has units of m/s — metres per second. That's speed.
Rate of change = (change in y-axis quantity) ÷ (change in x-axis quantity)
Always write the units of your gradient answer. "The gradient is 4" is incomplete. "The gradient is 4 m/s" tells the reader what it actually means.
Worked example — distance-time graph
EXAMPLE
On a distance-time graph, a line passes through (0, 0) and (30, 240), where time is in seconds and distance is in metres. What is the speed?
Gradient = rise ÷ run = (240 − 0) ÷ (30 − 0) = 240 ÷ 30 =8 m/s.
What a negative gradient means in context
On a distance-time graph, a negative gradient means the object is moving back towards the starting point — its distance from the origin is decreasing. On a speed-time graph, a negative gradient means the object is decelerating (slowing down).
