Recognising graph shapes helps you identify the relationship between two variables quickly.
Straight line through the origin
Shape: A straight diagonal line starting from (0,0). Meaning: y is directly proportional to x. Doubling x doubles y. Examples: Hooke’s law (force vs extension, within the limit of proportionality). Ohm’s law (voltage vs current for a fixed resistor at constant temperature).
Straight line not through the origin
Shape: A straight diagonal line that crosses the y-axis above or below zero. Meaning: y has a linear relationship with x, but not direct proportion. There is a constant offset. Example: Temperature conversion between Celsius and Fahrenheit.
Horizontal line
Shape: A flat line parallel to the x-axis. Meaning: y does not change as x changes. The quantity is constant. Examples: Constant temperature during a change of state (melting or boiling on a heating curve). Terminal velocity on a velocity-time graph.
Curve that levels off
Shape: Starts steep and gradually flattens to a horizontal asymptote. Meaning: y increases but at a decreasing rate, approaching a maximum. Examples: Charging a capacitor (voltage vs time). Cooling curve approaching room temperature (temperature vs time).
Exponential decay
Shape: A curve that drops steeply at first and then levels off, never quite reaching zero. Meaning: y decreases by a constant fraction in equal time intervals. Examples: Radioactive decay (activity vs time). Discharge of a capacitor (voltage vs time, Extended only).
Inverse proportion curve
Shape: A curve where y decreases as x increases, with the product x times y remaining constant. The curve approaches both axes but never touches them. Meaning: y is inversely proportional to x. Examples: Pressure vs volume at constant temperature (Boyle’s law). Frequency vs wavelength at constant wave speed.
Distance-time graph shapes
- Horizontal line: Object is stationary.
- Straight diagonal line: Object moves at constant speed.
- Upward curve (increasing gradient): Object is accelerating.
Velocity-time graph shapes
- Horizontal line: Constant velocity.
- Straight line going up: Constant acceleration.
- Straight line going down: Constant deceleration.
- Curve: Changing acceleration (e.g., object reaching terminal velocity).
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