Math 1 · Unit 3 · Lesson 5 · part 3 of 6
Is it linear? The constant rate of change
Not every situation makes a line.
Is it linear? The constant rate of change
Not every situation makes a line. A story is linear when it changes by the same amount every step: a constant rate of change. If the rate itself changes, growing or shrinking as you go, it is not linear.
| week | dollars | change |
|---|---|---|
| 0 | 40 | |
| 1 | 55 | +15 |
| 2 | 70 | +15 |
| 3 | 85 | +15 |
| week | dollars | change |
|---|---|---|
| 0 | 40 | |
| 1 | 50 | +10 |
| 2 | 70 | +20 |
| 3 | 110 | +40 |
The testDown a table with equal x steps, subtract each y from the next. All the same difference: linear, and that difference over the step is m. Different differences: not linear. (The second table doubles its change each week. That is the exponential family, coming later.)