Mathematical processing of graphical data

Sometimes a graph in its original form does not show quantitatively whether a prediction was right.

For example, a graph of mass produced against time, does not give you direct data to show how the rate of decay of milk changes with time. The data needs to be processed mathematically first.

Calculating the gradient

For a straight line graph:

\text{gradient} = \frac{\text{change in value on the vertical axis}}{\text{change in value on the horizontal axis}}

For a curved graph draw a tangent to the line and then find its gradient.

A tangent line placed on a graph showing the relationship of carbon dioxide produced and temperature

The tangent line:

  • touches the curve at a single point
  • has the same gradient (slope) as the curve at this point

Use tangents at different times to determine the rate of reaction at these times. Then use this processed data to draw a conclusion.