Analysis: (ii) measurement of gradients and intercepts.

The idea

A straight-line graph carries quantitative information in its slope and where it crosses an axis. To measure a gradient, choose two points on the line of best fit that are far apart (not two plotted data points, which may sit off the line), read their coordinates carefully using the axis scales, and calculate gradient = change in y ÷ change in x, giving units of y-unit per x-unit. A larger separation reduces reading error. To find an intercept, read the value where the line crosses the chosen axis: the y-intercept is the y-value at x = 0, and the x-intercept is the x-value at y = 0. If an axis does not start at zero, extend the line of best fit to the true zero position before reading the intercept, and state the intercept with its unit. Where the relationship is not linear, a tangent drawn at the required point allows a gradient to be estimated.

What earns the marks

• Defines gradient as the change in the y-variable divided by the change in the x-variable, taken from the line of best fit.
• Explains that two widely separated points on the line should be used to reduce the effect of reading error.
• States that the gradient carries units of the y-axis unit per x-axis unit.
• Describes reading an intercept as the value where the line of best fit crosses the relevant axis, including its unit.
• Recognises that if an axis does not begin at zero, the line must be extended to the true zero before the intercept is read.
• Notes that a tangent at a point can be used to estimate the gradient of a curve.

Common mistakes and how to put them right

• Using two raw data points rather than points on the line of best fit.

  Put it right: Read coordinates from the drawn line so scatter is averaged out.

• Dividing the change in x by the change in y.

  Put it right: Gradient is change in y divided by change in x.

• Reading an intercept straight off a truncated axis without extending the line to zero.

  Put it right: Extrapolate the line of best fit to the true zero position first.

Exam tips

• Mark the two chosen points on the line clearly and show the coordinate values you read before calculating.
• Carry the units through the gradient calculation and simplify them, for example cm³ min⁻¹.
• When reading an intercept, check whether the axis starts at zero and extend the line if it does not.