Graphs & Data Interpretation — A/L Physics

Linear Relationship (y = mx + c) A relationship where a constant change in the independent variable produces a constant change in the dependent variable. The graph is a straight line. The gradient (slope) represents the rate of change, and the y-intercept represents the value of y when x = 0. Example: For a wire under tension, extension vs. load is linear within the elastic limit; gradient gives the spring constant.

Non-Linear Relationship A relationship where the rate of change is not constant. Common forms include quadratic (y ∝ x²), inverse (y ∝ 1/x), and exponential (y ∝ eˣ). To analyse these, you often linearise the graph by plotting transformed variables (e.g., y vs. x²). Example: Period T of a simple pendulum vs. length L is non-linear; plotting T² vs. L gives a straight line with gradient 4π²/g.