A Linear Model from Two Data Points

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.

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.