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Reading intercepts, false origins and systematic errors

Edexcel IAL Physics · WPH16 Practical Skills in Physics II

Intercepts often hold a physical quantity or reveal a systematic error. Reading them wrongly is one of the commonest Unit 6 mistakes.

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Read or calculate?

The y-intercept is the value of y at x = 0. Read it directly only if the x-axis on your graph starts at 0 (or the y-axis is drawn at x = 0).
If you used a false origin, the left-hand edge of the grid is not x = 0. Calculate instead: c = y - mx using a point on the line (not a data point off the line).
Do not extrapolate beyond the grid by eye; calculate.
On a log graph, the intercept is log k or ln y_0: convert with 10^c or e^c.

Intercepts that reveal systematic errors

Several core practicals have an intercept that tells you about a systematic error:

Practical	Expected	Intercept means
CP1: sqrt(h) against t	Through origin	t-intercept = delay in releasing the ball
CP7: R against l	Through origin	R-intercept = contact resistance
CP16: T² (or 1/f²) against m	Through origin	Effect of the spring's own mass
CP15: count rate against thickness	Background not subtracted	Count rate never falls to zero

Using the gradient anyway

A constant systematic offset changes the intercept but not the gradient. That is why constants are found from gradients rather than from single readings.

Worked example

In core practical 1, a graph of sqrt(h) / m⁰.5 against t / s passes through (0.300, 0.620) and (0.500, 1.063). Find g and the release delay.

Gradient = (1.063 - 0.620) / (0.500 - 0.300) = 2.215 m⁰.5 s^-1
h = (1/2)g(t - t_0)², so sqrt(h) = sqrt(g/2)(t - t_0): g = 2 x gradient² = 9.81 m/s²
t-intercept: t_0 = 0.300 - 0.620 / 2.215 = 0.0201 s

Answer: g = 9.81 m/s², delay = 20 ms

Key idea: Read the intercept only at x = 0; otherwise c = y - mx from a point on the line. Convert log intercepts with 10^c or e^c. Unexpected intercepts signal systematic errors; gradients are unaffected.

Check yourself

A line passes through (2.0, 5.6) and (6.0, 9.2) on a graph whose x-axis starts at 1.0. Find the y-intercept.
Show answer
3.8. m = (9.2 - 5.6) / (6.0 - 2.0) = 0.90; c = 5.6 - 0.90 x 2.0 = 3.8.
Find the gradient of the line through (0.300, 0.620) and (0.500, 1.063), to 3 s.f.
Show answer
2.22. (1.063 - 0.620) / 0.200 = 2.22.
With gradient 2.215 m⁰.5 s^-1 for sqrt(h) against t, find g in m/s², to 3 s.f.
Show answer
9.81 m/s². g = 2 x 2.215² = 9.81 m/s².
A graph of T² against added mass m for a spring has gradient 1.58 s²/kg and intercept 0.024 s². The intercept is caused by an effective extra mass. Find that mass in kg, to 2 s.f.
Show answer
0.015 kg. Extra mass = intercept / gradient = 0.024 / 1.58 = 0.0152 kg.
A log-log graph has intercept log k = -0.35. Find k, to 3 s.f.
Show answer
0.447. k = 10^-0.35 = 0.447.
A graph's x-axis starts at 0.40. Why is the y-value at the left edge not the y-intercept?
- Intercepts can only be read on log graphs
- The intercept is the value at x = 0, which is off the grid
- The left edge is always zero
- The gradient is negative
Show answer
The intercept is the value at x = 0, which is off the grid. Examiners report many errors from reading the intercept at a false origin.
In core practical 7, contact resistance gives a positive intercept on a graph of R against l. What happens to the value of ρ found from the gradient?
- It is too large
- It is too small
- It cannot be found
- It is unaffected
Show answer
It is unaffected. A constant offset shifts the line without changing its slope.

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