Mathematical processing of graphical data
Sometimes the graph in its original form does not show Results that can be expressed using numerical values. whether a A suggestion, based on a hypothesis of how a factor will affect an outcome. 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 A straight line that just touches a point on a curve. A tangent to a circle is perpendicular to the radius which meets the tangent. to the line and then find its gradient:
- 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.