M.3—Graphs, proportionality, gradients and intercepts

A direct proportion gives a straight line through the origin when the correct variables are plotted. For y = mx + c, m is the gradient and c is the y-intercept.

Choose axes from the model, use a scale that fills the grid, plot precise crosses and draw a justified best-fit line or curve. A non-zero intercept may reveal a background amount or systematic offset.

If gas volume is proportional to time, V/t stays constant and the V–t graph passes through the origin. If a line has points (2,5) and (6,13), m = 2 and c = 1.

A line that looks straight is not proof of direct proportionality unless the intercept and ratio support it.