Graphs reveal relationships that tables hide. A straight line through the origin shows direct proportion; its gradient gives a constant such as density, speed or the reciprocal of resistance. A straight line with an intercept shows a linear relationship with a starting value. Curves show changing rates; the gradient of a tangent gives the rate at that instant.
The area under a graph can also mean something: under a velocity–time graph it is distance, and under a force–extension graph it is work done. Always read the axes, units and scales carefully before interpreting, and state the meaning of the gradient in words.
Worked example
A graph of current (mA) against voltage (V) is a straight line through the origin with gradient 50 mA/V. What is the resistance?
- Gradient = I ÷ V = 0.05 A per V.
- Resistance R = V ÷ I = 1 ÷ 0.05.
Answer:R = 20 Ω.
Key words
- tangent
- a line touching a curve at one point
- intercept
- where a line crosses an axis
- area under a graph
- can represent a physical quantity
- trend
- the general direction of the data
New questions every time.