A graph is an argument. These conventions make the argument readable.
- Independent variable on the horizontal axis — what you chose to change
- Dependent variable on the vertical axis — what you measured
- Label both axes with units
- Scale evenly, and do not force the origin if your data does not support it
- Draw a best-fit line, not a dot-to-dot
The data
A student measured how far a spring stretched under different loads.
| Mass (g) | Stretch (cm) |
|---|---|
| 100 | 2.1 |
| 200 | 3.9 |
| 300 | 6.2 |
| 400 | 8.1 |
| 500 | 9.8 |
Questions
1. Which variable goes on which axis, and why?
Answer
Mass on the horizontal axis, because the student chose it. Stretch on the vertical axis, because it is what the spring did in response.
2. Plot the data and draw a best-fit line.
What yours should look like
A straight line rising left to right, passing close to every point — but not through all of them. A line that hits every point exactly usually means you joined the dots instead of fitting a line.
3. Calculate the slope, with units.
Answer
Using the first and last points:
Which says: every extra gram stretches the spring about 0.019 cm.
4. Predict the stretch at , and at . Which prediction do you trust more?
Answer
About at 250 g, and about at 2000 g.
Trust the first far more. 250 g sits inside the range that was measured — that is interpolation. 2000 g is four times beyond anything tested, and springs stop behaving linearly once stretched too far. That is extrapolation, and it is where predictions go to die.
5. One point sits furthest from your line. Should you erase it?
Answer
No. A point that does not fit is data, not a mistake. You may investigate it, repeat that measurement, or note it in your analysis — but removing a measurement because it is inconvenient is the single most serious thing you can do wrong in science.