All subjects · Biology · WBI13 Practical Skills in Biology I

Gradients, intercepts and rates from graphs

Edexcel IAL Biology · WBI13 Practical Skills in Biology I

The specification asks you to determine a relationship or a constant from a graph, for example a gradient using a large triangle, or a rate from a tangent.

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Gradient of a straight line

Gradient = change in y ÷ change in x = (y₂ - y₁) / (x₂ - x₁)

Use a large triangle covering more than half the line, with corners on easy-to-read grid points on the line (not data points that sit off the line).
Include the units: y unit per x unit (for example cm³ per minute).
A line sloping down has a negative gradient: keep the minus sign. The January 2025 report: omitting the minus sign 'is vital here to show the direction'.
A straight line through the origin means the DV is directly proportional to the IV; y = mx + c, where m is the gradient and c the intercept.

Rate from a curve: tangents

In CP4, product formed against time is a curve because substrate is used up. The initial rate is the gradient of a tangent drawn at time zero.

1. Lay a ruler touching the curve at the point (here, at the start) without cutting it.

2. Draw a long tangent.

3. Find its gradient with a large triangle.

Initial rates are used because later, falling substrate concentration (not the IV) limits the rate.

Intercepts and reading values

The intercept is where the line crosses an axis. In the water potential practical, the concentration where the line of percentage change in mass crosses zero is where the tissue neither gains nor loses water: its water potential equals that solution's.
Interpolation reads values between plotted points; extrapolation extends beyond them and is less reliable.
Show construction lines on the graph so the examiner can see your reading.

Worked example

A straight line passes through (2, 1.5) and (10, 7.5), where x is time in minutes and y is volume of oxygen in cm³. Calculate the rate.

Gradient = (7.5 - 1.5) / (10 - 2)
= 6.0 / 8 = 0.75

Answer: 0.75 cm³ min⁻¹

Key idea: Gradient = Δy ÷ Δx from a large triangle, with units and sign. Initial rate = gradient of a tangent at t = 0. Intercepts give values such as the water potential of tissue. Show construction lines.

Check yourself

A line passes through (0, 12) and (40, 42), where x is time / s and y is volume / mm³. Calculate the gradient.
Show answer
0.75 mm³ s⁻¹. (42 - 12) / (40 - 0) = 30 / 40 = 0.75 mm³ s⁻¹.
A straight line on a graph of mass needed to break a fibre against fibre length passes through (10, 900) and (50, 500), with x = length / cm and y = mass / g. Calculate the gradient, including its sign.
Show answer
-10 g cm⁻¹. (500 - 900) / (50 - 10) = -400 / 40 = -10 g per cm. The minus sign shows mass to break falls as length increases.
Why should a large triangle be used to find a gradient?
- It makes the gradient steeper
- It reduces the percentage uncertainty in reading the changes
- It removes anomalous points
- It is needed to find the intercept
Show answer
It reduces the percentage uncertainty in reading the changes. Larger Δy and Δx are read with smaller percentage uncertainty.
How is the initial rate found from a curve of product against time?
- Divide the final product by the total time
- Read the y value at the end
- Draw a tangent at time zero and calculate its gradient
- Find the area under the curve
Show answer
Draw a tangent at time zero and calculate its gradient. The tangent at t = 0 gives the rate before substrate runs low.
Why are initial rates used in enzyme experiments (CP4)?
- Later, the falling substrate concentration limits the rate
- Enzymes only work for a few seconds
- The colorimeter warms up later
- Initial rates are always zero
Show answer
Later, the falling substrate concentration limits the rate. Substrate is used up, so later rates do not reflect the IV alone.
Percentage change in mass of potato is +2.0% in 0.30 mol dm⁻³ sucrose and -3.0% in 0.40 mol dm⁻³. Assuming a straight line between these points, estimate the concentration where there is no change in mass (2 d.p.).
Show answer
0.34 mol dm⁻³. Zero lies 2.0 / 5.0 of the way from 0.30 to 0.40: 0.30 + 0.10 x 0.4 = 0.34 mol dm⁻³.
A graph has the equation y = 0.25x + 3. What is the value of the intercept on the y axis?
- 3
- 0.25
- 0
- 12
Show answer
3. In y = mx + c, c is the intercept.

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Last updated 8 November 2026. Spotted a mistake? Tell us.