S1.3.5—Graphing

Build a graph that exposes the relationship

Put the independent variable on the horizontal axis, label both axes with quantity and unit, choose scales that use the plotting area, and show uncertainty bars where available. Use a line or curve of best fit for the trend; do not join each point.

Predicted model	Plot for a straight line	Gradient	Intercept
$y=kx$	$y$ against $x$	$k$	expected $0$
$y=kx^2$	$y$ against $x^2$	$k$	expected $0$
$y=k/x$	$y$ against $1/x$	$k$	expected $0$
$y=Ax^n$	$\log y$ against $\log x$	$n$	$\log A$

Extract meaning from the fit

Calculate gradient from two well-separated points on the best-fit line and include its units. Use maximum- and minimum-gradient acceptable lines through the uncertainty bars to estimate gradient uncertainty; apply the same idea to intercepts. Interpolate within the measured range cautiously; extrapolation relies on the model continuing beyond the evidence.

Example — test an exponential claim

For exponential decay, equal time intervals should give approximately the same multiplicative factor (or a constant half-life). Alternatively, a suitable logarithmic transformation should be linear. Agreement must be judged with the uncertainty bars, not from visual closeness alone.

Interpret, do not merely describe

A gradient is a rate of change; a changing gradient shows a changing rate; an intercept is the predicted value at zero input; maxima/minima are turning points; and an area under a graph is an accumulated quantity only when the product of the axis units represents that quantity.

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Calculate carefully

Rearrange symbolically, resolve vectors, convert units and use proportional reasoning before substituting.

Report evidence

Propagate uncertainty with the correct operation, then use labelled graphs, error bars, gradients, intercepts and areas to test the model.

S1.3.5—Graphing

Read and Linearize Graphs

Retrieve Mathematical Practice

S1.3.5 Exam Analysis