Mathematical processing of graphical data

Sometimes the 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 reaction changes with time. The data needs to be processed mathematically first.

Calculating the gradient

For a straight line graph:

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

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

Tangent line on a graph.
  • the tangent line touches the curve at a single point
  • the tangent line 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.