M.5—Graphs, data transformation and rates of change

Translate between numerical, graphical and algebraic forms; choose an appropriate chart and calculate rate from a gradient or tangent when the relationship changes.

Put the explanatory variable on x, use a meaningful scale and state the interval for any gradient.

The initial tangent to a respiration curve gives the initial rate, while the overall endpoint difference gives an average rate.

A steeper-looking graph may result from unequal axis scales; inspect units and scale before comparing gradients.