The gradient of a graph at any point represents the rate of change of the $y$-quantity with respect to the $x$-quantity at that instant.
For a straight-line graph: the gradient is constant throughout. $$\text{Gradient} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$$
For a curve: the gradient changes at every point. To find it at a specific point, draw a tangent at that point and calculate its gradient.
Practical interpretations:
- On a distance-time graph: gradient = speed (m/s or km/h)
- On a speed-time graph: gradient = acceleration (m/s²)
- On a temperature-time graph: gradient = rate of temperature change
Drawing a tangent: use a ruler to draw a straight line that just touches the curve at the point, extending either side. Then pick two clearly readable points on the tangent to calculate the gradient.
Common error: using two points on the curve rather than on the tangent line, or reading the gradient with the axes in the wrong order.