A.3 Graphs

The same relationship can appear as prose, a table, an equation or a graph. Translate one representation at a time and preserve variables, units and direction of change.

Name the independent and dependent variables, identify constants and check a point from one form against another before inferring a trend.

A table showing rate increasing with substrate can become a graph of rate against concentration; a plateau in the graph means the increase is no longer proportional.

Changing representation does not add evidence; an attractive graph can still hide a sampling or scale problem.

Put the explanatory variable on the horizontal axis and the response on the vertical axis unless the question requires otherwise. Use units, even spacing and a scale that fills the plotting area.

Plot measured points rather than joining them automatically; add a best-fit line only when a model or relationship is justified.

For enzyme concentration versus initial rate, each point represents a measured pair; a curved trend should not be forced into a straight line.

A line through the origin is a hypothesis, not a default, and extrapolation beyond the measured range needs justification.

For y = mx + c, m is the change in y per unit change in x and c is the y-intercept. Units must be carried into both quantities.

Choose two well-separated points on the fitted line, calculate rise/run and use the intercept only within the model’s measured domain.

If oxygen production rises 4 units for each 2 °C, the slope is 2 units °C⁻¹; it does not mean temperature alone caused the change.

A straight trend over one range does not guarantee linearity outside it or prove the intercept is biologically attainable.

An intercept is where a fitted relationship crosses an axis. It can represent a threshold, baseline or model parameter only when the variables and units make that interpretation meaningful.

Read the axis scale carefully, distinguish measured from extrapolated intercepts and report uncertainty when the crossing is not directly observed.

A compensation point where net photosynthesis is zero can be estimated from a graph, but it should not be read beyond the measured light range without qualification.

An intercept caused by extending a line is not automatically a real zero or threshold.

A rate is change in the measured quantity per unit time or another independent variable. On a graph, the gradient is rise divided by run, with units that reveal the rate.

Use two points on the relevant line or curve, keep the time interval explicit and avoid mixing a secant average with an instantaneous rate.

If oxygen increases from 12 to 20 cm³ over 4 min, the average rate is 2 cm³ min⁻¹; a tangent at one moment may give a different instantaneous rate.

A steeper graph means a larger rate only when both axes and scales are comparable.

The gradient of a tangent gives the instantaneous rate at one point on a curve. The tangent should touch the curve locally, not simply connect distant data points.

Draw a small, well-positioned tangent, choose two far-apart points on that tangent, calculate rise/run and include the correct units.

A respiration curve that flattens has a smaller tangent gradient later, showing that the instantaneous rate is falling even if total oxygen uptake still rises.

A tangent is an estimate whose uncertainty depends on curve thickness, measurement scatter and how the line is drawn.