Analysing Graphs
- The gradient of a graph can be found by:
- In the case of a straight line graph: using a triangle and the equation for a straight line
- In the case of a curve: drawing a tangent to the graph
- The triangle should be as large as possible to minimise precision errors
- The equation for a straight line is y = mx + c, where:
- y = dependent variable
- x = independent variable
- m = slope
- c = y-intercept
- The gradient or slope is therefore : m = ∆y/∆x
- This example from Kinetics illustrates the calculation of rates from a curve
The gradient can be found at different points on a curve. Here it has been multiplied by 60 to convert it from minutes-1 to seconds-1
- In the case of curves you will need a ruler to line up against the curve at the point you want to measure the gradient:
Lining up a ruler against the curve is essential to drawing a tangent accurately
Examiner Tip
Be careful that you process the units correctly when finding the gradient. The gradient unit is the y-unit divided by the x-unit, so in the example above the gradient of the curve is measured in cm3 s-1