22.5 - Reading & Interpreting Graphs
What a graph-reading question looks like
- Once a graph is drawn (by you or printed on the paper), you may be asked to get information back out of it.
- There are two things you can be asked to do:
- Read a particular value off the line
- Describe the trend the line shows
A typical question
The graph shows how the rate of photosynthesis of some pondweed changes with light intensity.
(a) Use the graph to estimate the rate of photosynthesis at a light intensity of 50%. [2]
(b) Describe the relationship between light intensity and the rate of photosynthesis. [2]
Where the marks come from
- (a) Read a value off the line that matches the graph, to within half a small square (1 mark).
- (a) Draw construction lines on the graph showing where that reading came from (1 mark).
- (b) Give the direction - that as the light intensity increases, the rate increases (1 mark).
- (b) Back it with figures from the axes, and say where the line levels off (1 mark).
The construction lines in part (a) and the figures in part (b) are the marks most often missed - it's easy to write down a number or say "it goes up" and think the job is done.
Reading a value off a graph
- To find the rate at a given value, go up from that value on the x-axis until you reach the line, then go across to the y-axis and read off the value.
- Always draw both dashed construction lines - a number written on its own, with no lines to show where it came from, can lose the mark.
- Example: reading up from 50% on the x-axis to the line, then across to the y-axis, gives about 29 bubbles per minute.
Interpolation vs extrapolation
- Interpolation - Reading a value between your plotted points. This is fine.
- Extrapolation - Reading a value beyond your last point. This is risky, so avoid it unless the question asks for it.
- The danger with extrapolation is that you have no readings out there, so you're guessing the line carries on the same way when it might level off, drop, or bend.
- Examiner reports flag candidates who extend the line past their data, or back to the origin, where there are no points to support it.
Describing a trend
- A good trend answer needs three things:
- The direction the graph goes (increases or decreases)
- Some figures from the axes to back it up
- Any change in behaviour - such as where the line levels off or peaks
- Get all three in and the answer is complete.
A sentence frame keeps them in order
As [the independent variable] increases, [the dependent variable] increases / decreases, from [figure] to [figure], then levels off at [value].
- For a photosynthesis graph, that reads: "As the light intensity increases, the rate of photosynthesis increases, from 0 to about 40 bubbles per minute, then levels off at around 80%."
- That one sentence carries the direction, the figures, and the change - every mark the trend is worth.
Finding a gradient
- You may be asked for the gradient of a straight section of the line.
- Pick two points that sit on the line, then divide the change in the y-value by the change in the x-value.
Formula for gradient:
Read both points off using construction lines, so the values you divide are ones the examiner can check.
The gradient is on the syllabus skills list, but it has not been asked on Paper 6 since at least 2019, so learn the two-point method and move on.
Common exam questions
Question 1
What is the difference between interpolation and extrapolation?
Interpolation is reading a value between your plotted points, which is fine; extrapolation is reading a value beyond your last point, which is risky.
Question 2
Why is extrapolation risky?
Because there are no readings that far along, so you are assuming the line carries on the same way when it might level off, drop, or bend; the pattern beyond the data is not known.
Question 3
What three things does a good description of a trend need?
The direction the line goes, some figures from the axes to back it up, and any change in behaviour, such as where the line levels off or peaks.
Question 4
When may you describe a relationship as "proportional"?
Only when the line is straight and passes through the origin; using it for a curved or offset line can cancel an otherwise correct answer.
Question 5
A student describes a trend by writing "the rate goes up". Why does this not get full marks?
It gives a direction but no figures from the axes and no mention of where the line levels off, so it is missing two of the three things a trend answer needs.
Question 6
How do you find the gradient of a straight section of a line?
Pick two points that lie on the line, then divide the change in the y-value by the change in the x-value, reading both points off with construction lines.