A candle is 14 cm tall when lit. Its height is measured every hour: (0 h, 14 cm), (1 h, 12 cm), (2 h, 10 cm), (3 h, 8 cm). Step 1: Check the output differences: 12 - 14 = -2, 10 - 12 = -2, 8 - 10 = -2. Step 2: The difference is the same every step - the rate of change is constant, -2 cm per hour. That is the signature of a linear function. Step 3: Plot the four points in words: they sit on one straight line slanting downward. A function is linear exactly when its points line up like this. Say it plainly: linear is not a compliment meaning "nice and increasing" - it is a precise claim: equal input steps always produce equal output steps.

A plant's height is measured weekly: (0, 3 cm), (1, 5 cm), (2, 7 cm), (3, 9 cm). Is height a linear function of time? -> Yes - differences are +2, +2, +2: a constant rate of change of 2 cm per week.