A supplied linear model on 0 ≤ t ≤ 8 has points (2, 11) and (5, 17), in minutes and liters. Rate = (17 − 11) ÷ (5 − 2) = 2 liters per minute. At two minutes, 4 liters come from change after the start, so b = 11 − 4 = 7 liters. The rule V = 2t + 7 matches both observations. Calling 11 the start would count the two-minute change twice.
For a decrease, subtract the signed changing part: on 0 ≤ t ≤ 6, if m = −2 liters per minute and V = 9 liters at t = 3, then b = 9 − (−2 × 3) = 15 liters. The expression 15 − 2t returns 9 at minute 3. Subtracting a negative change adds its magnitude.
Your new practice
A supplied linear model of water remaining, valid from 0 to 6 minutes, has rate −1.5 liters per minute and 16 liters at minute 2. Find its total at zero, write a rule and check the two-minute value. Predict the amount at minute 5. Explain what the negative sign belongs to.
Your calculation, rule and interpretation
Use b = observed output − m × observed input. If zero is outside the stated domain, the expression’s value there need not be a modeled starting amount.