College Algebra / Unit 6 Alg 308 worked example, 60 to 90 seconds
A Linear Model from Two Data Points
The idea
Building a linear model from two data points means converting the observations to coordinate pairs, running the two-point build, and reading the slope and intercept back as rate and start.
In practice
A seedling measures 4 cm on day 2 and 10 cm on day 5. As points: (2, 4) and (5, 10). Slope: (10 − 4)/(5 − 2) = 2 — the plant grows 2 cm per day. Point-slope from (2, 4): h(t) = 2t, so the intercept is 0: the model says the seedling broke soil at day zero. Check on the unused point: h(5) = 10 — agreement. Then read the model back into the world: rate 2 cm per day, start 0 cm. A model earns trust twice — once against the unused data point, once against the situation's plain sense.
Where people slip
The model interpolates with confidence and extrapolates on credit.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Builds on
- Nothing. This is a starting point.
Unlocks
- Nothing yet depends on this.
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