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Initial Value from a Table — Easy Worksheet 2
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 |
|---|---|
| 1 | 9 |
| 2 | 10 |
| 3 | 11 |
| 4 | 12 |
Not quite. The answer is
💡 Change in y = 10 − 9 = 1. Change in x = 2 − 1 = 1. Rate of change = 1 ÷ 1 = 1. Going back 1 from x = 1 to x = 0 subtracts the rate 1 time: y = 9 − 1 × 1 = 9 − 1 = 8. The initial value is 8.
✓ Correct!
Not quite. The answer is
💡 Change in y = 10 − 9 = 1. Change in x = 2 − 1 = 1. Rate of change = 1 ÷ 1 = 1. Going back 1 from x = 1 to x = 0 subtracts the rate 1 time: y = 9 − 1 × 1 = 9 − 1 = 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 |
|---|---|
| 1 | 4 |
| 2 | 8 |
| 3 | 12 |
| 4 | 16 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| x | y |
|---|---|
| 3 | 25 |
| 4 | 31 |
| 5 | 37 |
| 6 | 43 |
Not quite. The answer is
💡 Change in y = 31 − 25 = 6. Change in x = 4 − 3 = 1. Rate of change = 6 ÷ 1 = 6. Going back 3 from x = 3 to x = 0 subtracts the rate 3 times: y = 25 − 6 × 3 = 25 − 18 = 7. The initial value is 7.
✓ Correct!
Not quite. The answer is
💡 Change in y = 31 − 25 = 6. Change in x = 4 − 3 = 1. Rate of change = 6 ÷ 1 = 6. Going back 3 from x = 3 to x = 0 subtracts the rate 3 times: y = 25 − 6 × 3 = 25 − 18 = 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 |
|---|---|
| 1 | 15 |
| 2 | 17 |
| 3 | 19 |
| 4 | 21 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| x | y |
|---|---|
| 1 | 5 |
| 2 | 9 |
| 3 | 13 |
| 4 | 17 |
Not quite. The answer is
💡 Change in y = 9 − 5 = 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 = 5 − 4 × 1 = 5 − 4 = 1. The initial value is 1.
✓ Correct!
Not quite. The answer is
💡 Change in y = 9 − 5 = 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 = 5 − 4 × 1 = 5 − 4 = 1. The initial value is 1.
💡 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 | 2 |
| 2 | 3 |
| 3 | 4 |
| 4 | 5 |
✓ 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 | 12 |
| 3 | 15 |
| 4 | 18 |
Not quite. The answer is
💡 Change in y = 12 − 9 = 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 = 9 − 3 × 1 = 9 − 3 = 6. The initial value is 6.
✓ Correct!
Not quite. The answer is
💡 Change in y = 12 − 9 = 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 = 9 − 3 × 1 = 9 − 3 = 6. The initial value is 6.
💡 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 | 10 |
| 2 | 15 |
| 3 | 20 |
| 4 | 25 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| x | y |
|---|---|
| 3 | 12 |
| 4 | 14 |
| 5 | 16 |
| 6 | 18 |
Not quite. The answer is
💡 Change in y = 14 − 12 = 2. Change in x = 4 − 3 = 1. Rate of change = 2 ÷ 1 = 2. Going back 3 from x = 3 to x = 0 subtracts the rate 3 times: y = 12 − 2 × 3 = 12 − 6 = 6. The initial value is 6.
✓ Correct!
Not quite. The answer is
💡 Change in y = 14 − 12 = 2. Change in x = 4 − 3 = 1. Rate of change = 2 ÷ 1 = 2. Going back 3 from x = 3 to x = 0 subtracts the rate 3 times: y = 12 − 2 × 3 = 12 − 6 = 6. The initial value is 6.
💡 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 | 19 |
| 2 | 24 |
| 3 | 29 |
| 4 | 34 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| x | y |
|---|---|
| 2 | 11 |
| 3 | 14 |
| 4 | 17 |
| 5 | 20 |
Not quite. The answer is
💡 Change in y = 14 − 11 = 3. Change in x = 3 − 2 = 1. Rate of change = 3 ÷ 1 = 3. Going back 2 from x = 2 to x = 0 subtracts the rate 2 times: y = 11 − 3 × 2 = 11 − 6 = 5. The initial value is 5.
✓ Correct!
Not quite. The answer is
💡 Change in y = 14 − 11 = 3. Change in x = 3 − 2 = 1. Rate of change = 3 ÷ 1 = 3. Going back 2 from x = 2 to x = 0 subtracts the rate 2 times: y = 11 − 3 × 2 = 11 − 6 = 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 |
|---|---|
| 2 | 8 |
| 3 | 11 |
| 4 | 14 |
| 5 | 17 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| x | y |
|---|---|
| 2 | 9 |
| 3 | 11 |
| 4 | 13 |
| 5 | 15 |
Not quite. The answer is
💡 Change in y = 11 − 9 = 2. Change in x = 3 − 2 = 1. Rate of change = 2 ÷ 1 = 2. Going back 2 from x = 2 to x = 0 subtracts the rate 2 times: y = 9 − 2 × 2 = 9 − 4 = 5. The initial value is 5.
✓ Correct!
Not quite. The answer is
💡 Change in y = 11 − 9 = 2. Change in x = 3 − 2 = 1. Rate of change = 2 ÷ 1 = 2. Going back 2 from x = 2 to x = 0 subtracts the rate 2 times: y = 9 − 2 × 2 = 9 − 4 = 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 |
|---|---|
| 2 | 19 |
| 3 | 24 |
| 4 | 29 |
| 5 | 34 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| x | y |
|---|---|
| 2 | 18 |
| 3 | 24 |
| 4 | 30 |
| 5 | 36 |
Not quite. The answer is
💡 Change in y = 24 − 18 = 6. Change in x = 3 − 2 = 1. Rate of change = 6 ÷ 1 = 6. Going back 2 from x = 2 to x = 0 subtracts the rate 2 times: y = 18 − 6 × 2 = 18 − 12 = 6. The initial value is 6.
✓ Correct!
Not quite. The answer is
💡 Change in y = 24 − 18 = 6. Change in x = 3 − 2 = 1. Rate of change = 6 ÷ 1 = 6. Going back 2 from x = 2 to x = 0 subtracts the rate 2 times: y = 18 − 6 × 2 = 18 − 12 = 6. The initial value is 6.
💡 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 | 29 |
| 4 | 35 |
| 5 | 41 |
| 6 | 47 |
✓ 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 2
Each table shows a linear function. Find its initial value, the value of y when x = 0.