The straight-line model
Answers are for parents and teachers.
1
A table has x = 0, 1, 2, 3 and y = 15, 17, 19, 21. Find w and b and write the model.
| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | x | 0 | 1 | 2 | 3 |
| 2 | y | 15 | 17 | 19 | 21 |
b = 15 (y at x = 0) and w = 2 (the step). The model is y = 2x + 15.
2
Calculate y for w = 3, b = 10 and x = 4. Then for x = 0.
3 × 4 + 10 = 22. For x = 0: 10, which is b.
3
A table starts at x = 1: x = 1 gives y = 50 and x = 2 gives y = 60. Find w and b.
w = 10 (60 - 50). To find b go back one step: 50 - 10 = 40, so b = 40.
4
A bus card holds 20 units and each ride uses 2. Write the model, find y for 5 rides and say why 11 rides gives a result that cannot be right.
y = -2x + 20. For 5 rides y = 10. For 11 rides y = -2, but money left cannot be below 0: the model is wrong outside its sensible range.
5
In your own words, what is the difference between w and b typed by a person and w and b found by training?
A person chooses typed numbers by hand. In training the computer tries values, measures the mistakes and adjusts w and b by itself to make them smaller.