How to draw and use a physics graph
Choose scales that use more than half the grid, with 1, 2 or 5 units to each 2 cm square, and label each axis with the quantity and unit, like force / N. Plot every point to within half a small square. Circle the anomalous result and leave it out of the line. Draw one thin straight line with the points spread evenly on both sides. For the gradient, draw a triangle on the line that covers at least half of it. A straight line through the origin means the two quantities are directly proportional.
How answers are marked: a gradient counts within 5% of the least-squares line through the good points, and values you read off the line count within the spread of those lines plus half a small square. Plot the points for me draws your graph on screen; on paper the grid is blank, so you choose the scales.
Example: a spring
In set SPRNG2, the spring is 6.0 cm long and 20.8 cm with 4.0 N on it, so its extension is 20.8 − 6.0 = 14.8 cm. The 3.0 N result is anomalous: it sits well off the line through the others. The line of best fit rises about 6.0 N over 22.1 cm, a gradient of 0.272 N/cm, so the spring constant is 0.272 × 100 = 27.2 N/m. Open set SPRNG2
Questions
How do you draw a line of best fit in physics?
Use a sharp pencil and a ruler. Draw one thin straight line (or a smooth curve if the points clearly curve) with about the same number of points on each side along its whole length. It does not have to go through any point, or through the origin. Ignore any anomalous result.
How do you find the gradient of a graph?
Draw a large right-angled triangle on your line, covering at least half of it. Gradient = vertical side ÷ horizontal side, using the axis values, not the number of squares. Give it to 2 or 3 significant figures, with units.
How do you find the spring constant from a graph?
For a graph of force against extension, the spring constant is the gradient. If the extension is in cm, the gradient is in N/cm: multiply by 100 to get N/m. On a graph of extension against force, k = 1 ÷ gradient.
What is an anomalous result?
A result that does not fit the pattern of the others, for example a point well off the line through the rest. Circle it, leave it out of the line of best fit, and repeat the measurement if you can.
How do you know if two quantities are directly proportional?
The graph is a straight line that passes through the origin. A straight line that does not pass through the origin shows a linear relationship, but not direct proportion.
How do you find the focal length from a 1/v against 1/u graph?
For 1/u + 1/v = 1/f, the line meets the 1/v axis at 1/f, and has a gradient of about −1. Read the intercept and take 1 ÷ intercept to get f in the same unit as u and v.
Sources, read October 27, 2026: AQA GCSE Physics 8463 specification (required practicals 3, 4 and 6; anomalous results; F = ke); Cambridge IGCSE Physics 0625 syllabus for 2026 to 2028 (the 2029 syllabus says the same; drawing and analysing graphs: scales, plotting to half a small square, best-fit lines, a gradient triangle over at least half the line, 2 or 3 significant figures). g = 9.81 m/s².