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Initial Value from a Table — Easy Worksheet 1
Grade 8 · Whoobee Name: ____________________ Date: __________
Each table shows a linear function. Find its initial value, the value of y when x = 0.
How to solve
First find the rate of change: (change in y) ÷ (change in x). Then start from the row closest to x = 0 and work back to x = 0: subtract the rate of change once for every step you move back (or add it for every step you move forward from a negative x). The y-value you reach at x = 0 is the initial value.
Example
What is the initial value of the function in the table?
| x | y |
|---|---|
| 2 | 13 |
| 3 | 14 |
| 4 | 15 |
| 5 | 16 |
Answer: 11
| x | y |
|---|---|
| 2 | 23 |
| 3 | 27 |
| 4 | 31 |
| 5 | 35 |
Not quite. The answer is
💡 Change in y = 27 − 23 = 4. Change in x = 3 − 2 = 1. Rate of change = 4 ÷ 1 = 4. Going back 2 from x = 2 to x = 0 subtracts the rate 2 times: y = 23 − 4 × 2 = 23 − 8 = 15. The initial value is 15.
✓ Correct!
Not quite. The answer is
💡 Change in y = 27 − 23 = 4. Change in x = 3 − 2 = 1. Rate of change = 4 ÷ 1 = 4. Going back 2 from x = 2 to x = 0 subtracts the rate 2 times: y = 23 − 4 × 2 = 23 − 8 = 15. The initial value is 15.
💡 How to solve: Initial Value from a Table
First find the rate of change: (change in y) ÷ (change in x). Then start from the row closest to x = 0 and work back to x = 0: subtract the rate of change once for every step you move back (or add it for every step you move forward from a negative x). The y-value you reach at x = 0 is the initial value.
Try a similar one
What is the initial value of the function in the table?
| x | y |
|---|---|
| 3 | 10 |
| 4 | 11 |
| 5 | 12 |
| 6 | 13 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| x | y |
|---|---|
| 1 | 10 |
| 2 | 12 |
| 3 | 14 |
| 4 | 16 |
Not quite. The answer is
💡 Change in y = 12 − 10 = 2. Change in x = 2 − 1 = 1. Rate of change = 2 ÷ 1 = 2. Going back 1 from x = 1 to x = 0 subtracts the rate 1 time: y = 10 − 2 × 1 = 10 − 2 = 8. The initial value is 8.
✓ Correct!
Not quite. The answer is
💡 Change in y = 12 − 10 = 2. Change in x = 2 − 1 = 1. Rate of change = 2 ÷ 1 = 2. Going back 1 from x = 1 to x = 0 subtracts the rate 1 time: y = 10 − 2 × 1 = 10 − 2 = 8. The initial value is 8.
💡 How to solve: Initial Value from a Table
First find the rate of change: (change in y) ÷ (change in x). Then start from the row closest to x = 0 and work back to x = 0: subtract the rate of change once for every step you move back (or add it for every step you move forward from a negative x). The y-value you reach at x = 0 is the initial value.
Try a similar one
What is the initial value of the function in the table?
| x | y |
|---|---|
| 3 | 15 |
| 4 | 17 |
| 5 | 19 |
| 6 | 21 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| x | y |
|---|---|
| 1 | 9 |
| 2 | 11 |
| 3 | 13 |
| 4 | 15 |
Not quite. The answer is
💡 Change in y = 11 − 9 = 2. Change in x = 2 − 1 = 1. Rate of change = 2 ÷ 1 = 2. Going back 1 from x = 1 to x = 0 subtracts the rate 1 time: y = 9 − 2 × 1 = 9 − 2 = 7. The initial value is 7.
✓ Correct!
Not quite. The answer is
💡 Change in y = 11 − 9 = 2. Change in x = 2 − 1 = 1. Rate of change = 2 ÷ 1 = 2. Going back 1 from x = 1 to x = 0 subtracts the rate 1 time: y = 9 − 2 × 1 = 9 − 2 = 7. The initial value is 7.
💡 How to solve: Initial Value from a Table
First find the rate of change: (change in y) ÷ (change in x). Then start from the row closest to x = 0 and work back to x = 0: subtract the rate of change once for every step you move back (or add it for every step you move forward from a negative x). The y-value you reach at x = 0 is the initial value.
Try a similar one
What is the initial value of the function in the table?
| x | y |
|---|---|
| 3 | 17 |
| 4 | 18 |
| 5 | 19 |
| 6 | 20 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| x | y |
|---|---|
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |
| 4 | 12 |
Not quite. The answer is
💡 Change in y = 6 − 3 = 3. Change in x = 2 − 1 = 1. Rate of change = 3 ÷ 1 = 3. Going back 1 from x = 1 to x = 0 subtracts the rate 1 time: y = 3 − 3 × 1 = 3 − 3 = 0. The initial value is 0.
✓ Correct!
Not quite. The answer is
💡 Change in y = 6 − 3 = 3. Change in x = 2 − 1 = 1. Rate of change = 3 ÷ 1 = 3. Going back 1 from x = 1 to x = 0 subtracts the rate 1 time: y = 3 − 3 × 1 = 3 − 3 = 0. The initial value is 0.
💡 How to solve: Initial Value from a Table
First find the rate of change: (change in y) ÷ (change in x). Then start from the row closest to x = 0 and work back to x = 0: subtract the rate of change once for every step you move back (or add it for every step you move forward from a negative x). The y-value you reach at x = 0 is the initial value.
Try a similar one
What is the initial value of the function in the table?
| x | y |
|---|---|
| 2 | 19 |
| 3 | 21 |
| 4 | 23 |
| 5 | 25 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| x | y |
|---|---|
| 3 | 9 |
| 4 | 12 |
| 5 | 15 |
| 6 | 18 |
Not quite. The answer is
💡 Change in y = 12 − 9 = 3. Change in x = 4 − 3 = 1. Rate of change = 3 ÷ 1 = 3. Going back 3 from x = 3 to x = 0 subtracts the rate 3 times: y = 9 − 3 × 3 = 9 − 9 = 0. The initial value is 0.
✓ Correct!
Not quite. The answer is
💡 Change in y = 12 − 9 = 3. Change in x = 4 − 3 = 1. Rate of change = 3 ÷ 1 = 3. Going back 3 from x = 3 to x = 0 subtracts the rate 3 times: y = 9 − 3 × 3 = 9 − 9 = 0. The initial value is 0.
💡 How to solve: Initial Value from a Table
First find the rate of change: (change in y) ÷ (change in x). Then start from the row closest to x = 0 and work back to x = 0: subtract the rate of change once for every step you move back (or add it for every step you move forward from a negative x). The y-value you reach at x = 0 is the initial value.
Try a similar one
What is the initial value of the function in the table?
| x | y |
|---|---|
| 2 | 17 |
| 3 | 20 |
| 4 | 23 |
| 5 | 26 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| x | y |
|---|---|
| 3 | 17 |
| 4 | 21 |
| 5 | 25 |
| 6 | 29 |
Not quite. The answer is
💡 Change in y = 21 − 17 = 4. Change in x = 4 − 3 = 1. Rate of change = 4 ÷ 1 = 4. Going back 3 from x = 3 to x = 0 subtracts the rate 3 times: y = 17 − 4 × 3 = 17 − 12 = 5. The initial value is 5.
✓ Correct!
Not quite. The answer is
💡 Change in y = 21 − 17 = 4. Change in x = 4 − 3 = 1. Rate of change = 4 ÷ 1 = 4. Going back 3 from x = 3 to x = 0 subtracts the rate 3 times: y = 17 − 4 × 3 = 17 − 12 = 5. The initial value is 5.
💡 How to solve: Initial Value from a Table
First find the rate of change: (change in y) ÷ (change in x). Then start from the row closest to x = 0 and work back to x = 0: subtract the rate of change once for every step you move back (or add it for every step you move forward from a negative x). The y-value you reach at x = 0 is the initial value.
Try a similar one
What is the initial value of the function in the table?
| x | y |
|---|---|
| 1 | 9 |
| 2 | 12 |
| 3 | 15 |
| 4 | 18 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| x | y |
|---|---|
| 1 | 18 |
| 2 | 22 |
| 3 | 26 |
| 4 | 30 |
Not quite. The answer is
💡 Change in y = 22 − 18 = 4. Change in x = 2 − 1 = 1. Rate of change = 4 ÷ 1 = 4. Going back 1 from x = 1 to x = 0 subtracts the rate 1 time: y = 18 − 4 × 1 = 18 − 4 = 14. The initial value is 14.
✓ Correct!
Not quite. The answer is
💡 Change in y = 22 − 18 = 4. Change in x = 2 − 1 = 1. Rate of change = 4 ÷ 1 = 4. Going back 1 from x = 1 to x = 0 subtracts the rate 1 time: y = 18 − 4 × 1 = 18 − 4 = 14. The initial value is 14.
💡 How to solve: Initial Value from a Table
First find the rate of change: (change in y) ÷ (change in x). Then start from the row closest to x = 0 and work back to x = 0: subtract the rate of change once for every step you move back (or add it for every step you move forward from a negative x). The y-value you reach at x = 0 is the initial value.
Try a similar one
What is the initial value of the function in the table?
| x | y |
|---|---|
| 3 | 11 |
| 4 | 14 |
| 5 | 17 |
| 6 | 20 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| x | y |
|---|---|
| 1 | 6 |
| 2 | 10 |
| 3 | 14 |
| 4 | 18 |
Not quite. The answer is
💡 Change in y = 10 − 6 = 4. Change in x = 2 − 1 = 1. Rate of change = 4 ÷ 1 = 4. Going back 1 from x = 1 to x = 0 subtracts the rate 1 time: y = 6 − 4 × 1 = 6 − 4 = 2. The initial value is 2.
✓ Correct!
Not quite. The answer is
💡 Change in y = 10 − 6 = 4. Change in x = 2 − 1 = 1. Rate of change = 4 ÷ 1 = 4. Going back 1 from x = 1 to x = 0 subtracts the rate 1 time: y = 6 − 4 × 1 = 6 − 4 = 2. The initial value is 2.
💡 How to solve: Initial Value from a Table
First find the rate of change: (change in y) ÷ (change in x). Then start from the row closest to x = 0 and work back to x = 0: subtract the rate of change once for every step you move back (or add it for every step you move forward from a negative x). The y-value you reach at x = 0 is the initial value.
Try a similar one
What is the initial value of the function in the table?
| x | y |
|---|---|
| 2 | 23 |
| 3 | 27 |
| 4 | 31 |
| 5 | 35 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Initial Value from a Table — Easy Worksheet 1
Each table shows a linear function. Find its initial value, the value of y when x = 0.