Math 1 · Unit 7 · Lesson 5 · part 2 of 6
The table test: subtract, then divide
Lesson 1 gave you the one idea: lines add, exponentials multiply.
The table test: subtract, then divide
Lesson 1 gave you the one idea: lines add, exponentials multiply. Here is the test that turns it into a habit. It only works when the x column goes up by equal steps, so check that first.
- 1Check that x goes up by equal steps.0, 1, 2, 3 or 0, 5, 10, 15. If not, the test does not apply yet.
- 2Subtract each y from the next.All the differences the same? Linear. The constant difference is the slope, rise over run with the run being the x step.
- 3If not, divide each y by the one before.All the ratios the same? Exponential. The constant ratio is b.
- 4Neither the same?Neither family. (It might be the quadratic family from a later unit, or nothing you have met yet.)
| x | y | difference |
|---|---|---|
| 0 | 7 | |
| 1 | 10 | 3 |
| 2 | 13 | 3 |
| 3 | 16 | 3 |
| x | y | ratio |
|---|---|---|
| 0 | 7 | |
| 1 | 21 | 3 |
| 2 | 63 | 3 |
| 3 | 189 | 3 |
Do both checks before saying neither. A table whose differences change might still have a constant ratio. Subtract first; if that fails, divide.