Algebra 1 · Unit 5 · Topic 5.5
Linear Models, Units, and Reasonable Predictions
A linear model assumes a constant additive change in output for each unit change in input.
Definition and explanation
A linear model assumes a constant additive change in output for each unit change in input. Interpret both slope and intercept, and restrict predictions to contexts where that assumption is reasonable.
Worked example
A candle is 18 cm tall and loses 1.5 cm per hour while burning. Model its height by H(t) = 18 − 1.5t for 0 ≤ t ≤ 12 hours. At t = 4, H = 12 cm; solving H = 0 gives a modeled burn time of 12 hours.
Common mistake
Extending this model beyond 12 hours predicts negative height, which has no meaning for the candle.
Key takeaway
A linear model assumes a constant additive change in output for each unit change in input.
Explain each step of the worked example, then check the units, signs, and conditions that apply.
Further reading
Topic coverage was checked against the openly available OpenStax Elementary Algebra 2e and Algebra and Trigonometry 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.