A good graph turns a wall of numbers into a picture you can actually reason with. But a graph only earns its marks if it’s plotted properly — sensible axes, accurate points, a fair line of best fit — and then read correctly. This page covers plotting from scratch, drawing lines of best fit, and pulling real physics out of a graph through its gradient and the area underneath.
📚 What you need to know
Put the independent variable on the x-axis, the dependent on the y-axis
Choose linear scales so points fill at least half the grid
A line of best fit can be straight or curved, with points balanced either side
The gradient of a y–x graph is Δy/Δx
The area under a graph often equals a physical quantity
Non-linear relationships can be linearised to give a straight line
Plotting a graph properly
Marks are won and lost before you draw a single point, in how you set the graph up. Follow the same checklist every time.
⚛ Plotting checklist
Label both axes with the quantity and its unit.
Put the independent variable on the x-axis, the dependent on the y-axis.
Choose linear scales so the points fill at least half the grid.
Plot points accurately, using small crosses.
Draw a line of best fit — straight or smoothly curved.
Axes labelled with units, points marked as small crosses, and a straight line of best fit balanced through the data.
Lines of best fit
A line of best fit is not the same as a straight line — it can be a smooth curve if that’s the trend. What matters is that it captures the overall pattern, with the data points balanced on either side.
If straight, draw it with a ruler.
If curved, draw it smoothly and freehand — no kinks.
Only force it through the origin if the data genuinely supports it.
A subtle exam point: don’t join the dots! A line of best fit is a single smooth line that represents the trend, ignoring the small scatter. Beginners often connect every point in a zig-zag — that throws away the whole purpose of the line, which is to average out random uncertainty.
Reading the gradient
On a straight-line graph, the gradient is constant and often equals a physical quantity (a velocity-time graph’s gradient is acceleration, for instance).
Gradientm = Δy / Δx = (y2 − y1) / (x2 − x1)
To find it well: draw a large gradient triangle (small ones magnify reading errors), read the run and rise off the axes using points on the line (not stray data points), then divide.
WE 1
A straight line of best fit passes through (0.20 s, 4.0 m) and (1.60 s, 32.0 m) on a distance–time graph. Find the gradient and say what it represents.
Step 1 — rise over runm = (32.0 − 4.0) / (1.60 − 0.20) = 28.0 / 1.40Step 2 — evaluate
= 20 m s−1gradient = 20 m s−1 = the speedOn a distance-time graph the gradient IS the speed. The units come out as m/s automatically — another reason to track units.
Area under a graph
The area between a graph and the x-axis often represents a real physical quantity too. The classic case: the area under a velocity–time graph equals the displacement.
The shaded triangle under the line has area ½ × base × height = 80 m, which is the displacement.
For rectangles and triangles, use area = base × height (or ½ base × height). For a curve, split the region into strips — rectangles and triangles — and add them, or count squares.
WE 2
On a velocity–time graph, a straight line rises from rest to 20 m s−1 over 8.0 s. Find the displacement.
Step 1 — the area is a triangle
displacement = ½ × base × height
Step 2 — substitute
= ½ × 8.0 × 20 = 80 mdisplacement = 80 mArea under a v-t graph = displacement. The triangle’s base is the time and its height is the final velocity.
Linearising a graph
Straight lines are far easier to read than curves, so we often linearise a non-linear relationship — rearranging it to fit y = mx + c. For a pendulum, T = 2π√(L/g) is a curve, but plotting T² against L gives a straight line whose gradient is 4π²/g. That lets you find g cleanly from the slope.
💡 Top tips
Independent variable on x, dependent on y; label with units.
Scale so points fill at least half the grid.
Line of best fit balances the points — don’t join the dots.
Draw a big gradient triangle and use points on the line.
Area under a v–t graph = displacement; gradient = acceleration.
⚠ Common mistakes
Joining the dots instead of drawing a smooth best-fit line
Reading the gradient off data points rather than the line
Drawing a gradient triangle that’s too small
Choosing a scale that cramps the data into a corner
Forgetting the units of a gradient or area
Quick recap: Plot with the independent variable on x, sensible linear scales, and points as crosses. Draw a balanced line of best fit (don’t join dots). The gradient (Δy/Δx, big triangle) and the area underneath both give real physics. Linearise curves to turn them into straight lines.
You can now plot a graph and pull a gradient from it. The final piece is honesty about how reliable that gradient is — every plotted point carries an uncertainty, shown as an error bar, and those feed into the uncertainty of your gradient and intercept. That’s the last skill in this toolkit: Uncertainties from Graphs.
Graph questions costing you marks?
Book a free meeting and we’ll practise plotting cleanly, drawing best-fit lines, and reading gradients and areas — the graph skills that run right through the IA and both papers.
