Math 1 · Unit 10 · Lesson 2 · part 3 of 5
Read the model: slope, y-intercept, and predictions
The tool's line for the rat is very close to W = 100 + 40t , where W is the weight in grams after t weeks.
Read the model: slope, y-intercept, and predictions
The tool's line for the rat is very close to W = 100 + 40t, where W is the weight in grams after t weeks. Read it the Unit 3 way: what family, what are its numbers, and what does each number mean in the story?
- 1The slope, 40.Rise over run: 40 grams for each 1 week. The rat gains about 40 grams a week.
- 2The y-intercept, 100.The value when t = 0. The rat weighed about 100 grams at birth.
- 3Say "about".The points are not exactly on the line. The model gives a predicted value, what it says y should be, not a promise.
Forward: predict W from t
At 10 weeks: W = 100 + 40(10) = 500 grams.
Backward: find t from W
When does it reach 760 grams? 100 + 40t = 760. Subtract 100 from both sides: 40t = 660. Divide both sides by 40: t = 16.5 weeks. The Unit 1 moves.
Both of those predictions are outside the weeks that were measured (0 to 8). That matters.
Interpolate: predict inside the dataBetween the values you measured. Week 4.5, when you have data for weeks 0 to 8. Fairly safe, because the data surrounds it.
Extrapolate: predict outside the dataBeyond the values you measured. Week 10 is a little outside. Riskier the farther you go, because nothing says the pattern continues.
Always ask: does this prediction make sense? The model says a 5-year-old rat (260 weeks) would weigh 100 + 40 × 260 = 10,500 grams. That is more than 10 kilograms, heavier than most house cats. Not believable: rats stop growing. The line was only ever a good fit near the data.