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Linear or Nonlinear? (Tables) — Easy Worksheet 2
Grade 8 · Whoobee Name: ____________________ Date: __________
Write "linear" or "nonlinear" for each table.
How to solve
A function is linear when its rate of change is constant. Between each pair of neighbouring rows work out (change in y) ÷ (change in x). If it is the same every time, the function is linear; if it changes, the function is nonlinear. When x always goes up by the same step, it is enough to check that y changes by the same amount each time.
Example
Does the table show a linear or a nonlinear function?
| x | y |
|---|---|
| 0 | −2 |
| 1 | 1 |
| 2 | 4 |
| 3 | 7 |
| 4 | 10 |
Answer: linear
| x | y |
|---|---|
| 0 | 3 |
| 1 | 4 |
| 2 | 7 |
| 3 | 12 |
| 4 | 19 |
Not quite. The answer is
💡 x goes up by 1 each time and y changes by +1, +3, +5, +7. The changes are not all the same. The rate of change is not constant, so the function is nonlinear.
✓ Correct!
Not quite. The answer is
💡 x goes up by 1 each time and y changes by +1, +3, +5, +7. The changes are not all the same. The rate of change is not constant, so the function is nonlinear.
💡 How to solve: Linear or Nonlinear? (Tables)
A function is linear when its rate of change is constant. Between each pair of neighbouring rows work out (change in y) ÷ (change in x). If it is the same every time, the function is linear; if it changes, the function is nonlinear. When x always goes up by the same step, it is enough to check that y changes by the same amount each time.
Try a similar one
Does the table show a linear or a nonlinear function?
| x | y |
|---|---|
| 1 | 6 |
| 2 | 8 |
| 3 | 12 |
| 4 | 20 |
| 5 | 36 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| x | y |
|---|---|
| 0 | −5 |
| 1 | −4 |
| 2 | −3 |
| 3 | −2 |
| 4 | −1 |
Not quite. The answer is
💡 x goes up by 1 each time and y changes by +1, +1, +1, +1. The change is always the same. The rate of change is constant, so the function is linear.
✓ Correct!
Not quite. The answer is
💡 x goes up by 1 each time and y changes by +1, +1, +1, +1. The change is always the same. The rate of change is constant, so the function is linear.
💡 How to solve: Linear or Nonlinear? (Tables)
A function is linear when its rate of change is constant. Between each pair of neighbouring rows work out (change in y) ÷ (change in x). If it is the same every time, the function is linear; if it changes, the function is nonlinear. When x always goes up by the same step, it is enough to check that y changes by the same amount each time.
Try a similar one
Does the table show a linear or a nonlinear function?
| x | y |
|---|---|
| 0 | −3 |
| 1 | −2 |
| 2 | 0 |
| 3 | 4 |
| 4 | 12 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| x | y |
|---|---|
| 1 | −4 |
| 2 | −3 |
| 3 | −2 |
| 4 | −1 |
| 5 | 0 |
Not quite. The answer is
💡 x goes up by 1 each time and y changes by +1, +1, +1, +1. The change is always the same. The rate of change is constant, so the function is linear.
✓ Correct!
Not quite. The answer is
💡 x goes up by 1 each time and y changes by +1, +1, +1, +1. The change is always the same. The rate of change is constant, so the function is linear.
💡 How to solve: Linear or Nonlinear? (Tables)
A function is linear when its rate of change is constant. Between each pair of neighbouring rows work out (change in y) ÷ (change in x). If it is the same every time, the function is linear; if it changes, the function is nonlinear. When x always goes up by the same step, it is enough to check that y changes by the same amount each time.
Try a similar one
Does the table show a linear or a nonlinear function?
| x | y |
|---|---|
| 0 | 2 |
| 1 | 3 |
| 2 | 4 |
| 3 | 5 |
| 4 | 6 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| x | y |
|---|---|
| 0 | −1 |
| 1 | 0 |
| 2 | 3 |
| 3 | 8 |
| 4 | 15 |
Not quite. The answer is
💡 x goes up by 1 each time and y changes by +1, +3, +5, +7. The changes are not all the same. The rate of change is not constant, so the function is nonlinear.
✓ Correct!
Not quite. The answer is
💡 x goes up by 1 each time and y changes by +1, +3, +5, +7. The changes are not all the same. The rate of change is not constant, so the function is nonlinear.
💡 How to solve: Linear or Nonlinear? (Tables)
A function is linear when its rate of change is constant. Between each pair of neighbouring rows work out (change in y) ÷ (change in x). If it is the same every time, the function is linear; if it changes, the function is nonlinear. When x always goes up by the same step, it is enough to check that y changes by the same amount each time.
Try a similar one
Does the table show a linear or a nonlinear function?
| x | y |
|---|---|
| 0 | −6 |
| 1 | −1 |
| 2 | 4 |
| 3 | 9 |
| 4 | 14 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| x | y |
|---|---|
| 0 | −3 |
| 1 | −2 |
| 2 | 0 |
| 3 | 4 |
| 4 | 12 |
Not quite. The answer is
💡 x goes up by 1 each time and y changes by +1, +2, +4, +8. The changes are not all the same. The rate of change is not constant, so the function is nonlinear.
✓ Correct!
Not quite. The answer is
💡 x goes up by 1 each time and y changes by +1, +2, +4, +8. The changes are not all the same. The rate of change is not constant, so the function is nonlinear.
💡 How to solve: Linear or Nonlinear? (Tables)
A function is linear when its rate of change is constant. Between each pair of neighbouring rows work out (change in y) ÷ (change in x). If it is the same every time, the function is linear; if it changes, the function is nonlinear. When x always goes up by the same step, it is enough to check that y changes by the same amount each time.
Try a similar one
Does the table show a linear or a nonlinear function?
| x | y |
|---|---|
| 1 | 7 |
| 2 | 9 |
| 3 | 11 |
| 4 | 13 |
| 5 | 15 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| x | y |
|---|---|
| 1 | 8 |
| 2 | 13 |
| 3 | 18 |
| 4 | 23 |
| 5 | 28 |
Not quite. The answer is
💡 x goes up by 1 each time and y changes by +5, +5, +5, +5. The change is always the same. The rate of change is constant, so the function is linear.
✓ Correct!
Not quite. The answer is
💡 x goes up by 1 each time and y changes by +5, +5, +5, +5. The change is always the same. The rate of change is constant, so the function is linear.
💡 How to solve: Linear or Nonlinear? (Tables)
A function is linear when its rate of change is constant. Between each pair of neighbouring rows work out (change in y) ÷ (change in x). If it is the same every time, the function is linear; if it changes, the function is nonlinear. When x always goes up by the same step, it is enough to check that y changes by the same amount each time.
Try a similar one
Does the table show a linear or a nonlinear function?
| x | y |
|---|---|
| 1 | −1 |
| 2 | 0 |
| 3 | 1 |
| 4 | 2 |
| 5 | 3 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| x | y |
|---|---|
| 0 | 5 |
| 1 | 6 |
| 2 | 8 |
| 3 | 12 |
| 4 | 20 |
Not quite. The answer is
💡 x goes up by 1 each time and y changes by +1, +2, +4, +8. The changes are not all the same. The rate of change is not constant, so the function is nonlinear.
✓ Correct!
Not quite. The answer is
💡 x goes up by 1 each time and y changes by +1, +2, +4, +8. The changes are not all the same. The rate of change is not constant, so the function is nonlinear.
💡 How to solve: Linear or Nonlinear? (Tables)
A function is linear when its rate of change is constant. Between each pair of neighbouring rows work out (change in y) ÷ (change in x). If it is the same every time, the function is linear; if it changes, the function is nonlinear. When x always goes up by the same step, it is enough to check that y changes by the same amount each time.
Try a similar one
Does the table show a linear or a nonlinear function?
| x | y |
|---|---|
| 1 | 3 |
| 2 | 5 |
| 3 | 9 |
| 4 | 17 |
| 5 | 33 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| x | y |
|---|---|
| 0 | −3 |
| 1 | 0 |
| 2 | 3 |
| 3 | 6 |
| 4 | 9 |
Not quite. The answer is
💡 x goes up by 1 each time and y changes by +3, +3, +3, +3. The change is always the same. The rate of change is constant, so the function is linear.
✓ Correct!
Not quite. The answer is
💡 x goes up by 1 each time and y changes by +3, +3, +3, +3. The change is always the same. The rate of change is constant, so the function is linear.
💡 How to solve: Linear or Nonlinear? (Tables)
A function is linear when its rate of change is constant. Between each pair of neighbouring rows work out (change in y) ÷ (change in x). If it is the same every time, the function is linear; if it changes, the function is nonlinear. When x always goes up by the same step, it is enough to check that y changes by the same amount each time.
Try a similar one
Does the table show a linear or a nonlinear function?
| x | y |
|---|---|
| 0 | −4 |
| 1 | −2 |
| 2 | 0 |
| 3 | 2 |
| 4 | 4 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Linear or Nonlinear? (Tables) — Easy Worksheet 2
Write "linear" or "nonlinear" for each table.