What is the gradient of a graph?

• The gradient of a graph at any point is equal to the gradient of the tangent to the curve at that point
• Remember that a tangent is a line that just touches a curve (and doesn’t cross it)

How do I estimate the gradient under a graph?

• To find an estimate for the gradient:
  • Draw a tangent to the curve
  • Find the gradient of the tangent using Gradient = RISE ÷ RUN

  

  • • In the example above, the gradient at x = 4 would be 
• It is an estimate because the tangent has been drawn by eye and is not exact

What does the gradient represent?

• In a y-x graph, the gradient represents the rate of change of y against x
• This has many practical applications, for example;
  • in a distance-time graph, the gradient (rate of change of distance against time) is the speed
  • in a speed-time graph, the gradient (rate of change of speed against time) is the acceleration