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Graphs and slopes
Beginner
The slope of a graph gives a rate; the area under it gives an accumulated total.
A graph shows how one quantity depends on another. The slope gives the rate of change (units: y per x) and the area under it gives the accumulated product. Straight lines indicate proportionality; curves show nonlinear relations.
On a velocity–time graph the slope is acceleration and the area is displacement.
Check axis labels and scales before reading slopes. A steep line on a zoomed axis may be gentle in reality.
In more detail
A graph turns data into a picture. The slope of a straight-line graph gives a physical quantity, such as velocity from a position-time graph, and the intercept gives a starting value.
Real-world uses
- Plotting distance against time for a trolley experiment to find its speed.
- Pharmacists plot drug concentration against time to predict dosing.
- A graph of distance against time for a runner shows a steady slope for constant speed, and a steeper line means a faster runner.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
How do I choose the axes?
Put the quantity you control on the horizontal axis and the quantity you measure on the vertical axis.
Should a graph always pass through the origin?
Only if the physics says it must. Forcing it through zero when the data does not can hide a systematic error.
What does a curved graph tell me?
A changing slope means the rate of change is changing, such as an accelerating car on a distance-time graph.
Related topics in Measurement & Math Tools
Differential equations in physics · Taylor series and small angles · Complex numbers and phasors · Curve fitting and linearisation · Logarithmic scales