To test a proposed y = k × x rule, compare it with every displayed pair. For (1, 5), (2, 10), (3, 16), k = 5 fits the first two pairs, but 5 × 3 = 15, not 16. No single constant fits the whole displayed set. Do not change a recorded value merely to make a rule fit.
Your different practice
| Input x | Output y | y ÷ x for x greater than zero |
|---|---|---|
| 1 | 2 | |
| 2 | 4 | |
| 4 | 10 |
A fictional learner says, “The first pair gives k = 2, and the second agrees, so y = 2 × x fits the whole table.” Complete all three quotients, test the proposed rule at x = 4 and explain the conclusion. What remains unknown about an unshown input x = 3 if no rule is supplied?
Counterexample and limit