A.3 Graphs
- Syllabus
- 2021
- Topic
- —
- Level
- AS
Learning objectives
—A.3.1—Translating between data formsTranslate information between graphical, numerical and algebraic forms, including using data represented by dissociation curves.—A.3.2—Plotting two variablesPlot two variables from experimental or other data and select appropriate formats such as bar charts, histograms, graphs and scattergrams.—A.3.3—Linear relationshipsUnderstand that y = mx + c represents a linear relationship and predict or sketch linear graphs in biological contexts.—A.3.5—Rates from linear graphsCalculate rate of change from a graph showing a linear relationship, for example transpiration rate.—A.3.6—Tangents and instantaneous ratesDraw and use the slope of a tangent to a curve as a measure of rate of change, such as product formation at a point on an enzyme-reaction curve.
Translate between words, tables, equations and 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.
Choose and plot the graph that matches two variables
Choose a display from the variable types and the question before plotting. Put the independent/explanatory variable on the x-axis and the dependent/response variable on the y-axis unless a convention in the question overrides this.
| Data/question | Suitable display | Construction rule |
|---|---|---|
| Separate categories | Bar chart | Equal-width separated bars; usually start numerical axis at zero |
| Continuous measurements grouped into class intervals | Histogram | Touching bars; bar area represents frequency, so use frequency density if widths differ |
| Paired continuous measurements seeking association | Scattergram | Plot independent pairs; add best-fit line only when justified |
| Continuous response across ordered/continuous x values | Line graph or scatter with fitted curve | Plot points accurately; connect or fit according to the sampling/model |
Label both axes with quantity and unit, choose a linear or specified log scale that occupies most of the grid, plot every pair accurately and include error bars or a key when supplied. Do not extrapolate a fitted line to the origin unless the evidence or model requires it.
Histogram bars touch because intervals are continuous; category bars remain separate. A line through points implies an ordered relationship and must not be added automatically to categories.
Use y = mx + c to model a linear biological relationship
In y=mx+c, m=Δy/Δx is the constant change in response per unit change in the explanatory variable, and c is the y-intercept when x=0. Both carry units or biological meaning from the axes.
Draw a straight best-fit line only across a supported linear region. Choose two widely separated points on that line, calculate the signed gradient with a large triangle and read the intercept from the fitted line. Substitute both into the equation and test it against another point.
With excess enzyme and substrate well below saturation, rate may be proportional to substrate concentration, giving a line through or near the origin over that range. A cooling line with gradient −1.32 °C h−1 and intercept 99.0 °C is y=−1.32x+99.0; the negative sign shows cooling.
A straight section does not prove the relationship remains linear outside the measured range. If enzyme active sites become limiting, the substrate–rate graph curves toward a plateau and one global y=mx+c model is inappropriate.
Use graph intercepts only when the axes and model support them
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.
Calculate a rate from the gradient of a graph
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.
Use a tangent to estimate an instantaneous rate
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.