Math worksheet for determining proportionality using tables.

To determine if the values in each table are proportional, we need to check whether the ratio of Y to X (i.e., Y/X) is constant for all pairs in the table. If the ratio is the same for every row, then the relationship is proportional. If not, it’s not proportional.

We can also think of proportionality as:
> Y = k × X, where k is a constant (the constant of proportionality).

Let’s go through each table one by one.

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1) Table 1

| X | Y |
|----|----|
| -4 | -5 |
| -3 | -6 |
| -2 | -7 |
| -1 | -8 |

Check ratios:
- -5 / -4 = 1.25
- -6 / -3 = 2
- -7 / -2 = 3.5
- -8 / -1 = 8

→ Ratios are not constant → Not proportional

✔ Answer: No

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2) Table 2

| X | Y |
|---|---|
| 6 | -2 |
| 7 | -1 |
| 8 | 0 |
| 9 | 1 |

Ratios:
- -2 / 6 ≈ -0.333
- -1 / 7 ≈ -0.143
- 0 / 8 = 0
- 1 / 9 ≈ 0.111

→ Not constant → Not proportional

✔ Answer: No

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3) Table 3

| X | Y |
|-----|----|
| -20 | -10 |
| -56 | -8 |
| -14 | -2 |
| -7 | -1 |

Ratios:
- -10 / -20 = 0.5
- -8 / -56 ≈ 0.1429
- -2 / -14 ≈ 0.1429
- -1 / -7 ≈ 0.1429

First ratio is 0.5, others ~0.1429 → Not constant

✔ Answer: No

*(Note: The first pair doesn’t match the rest — so not proportional.)*

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4) Table 4

| X | Y |
|---|---|
| 6 | 3 |
| 7 | 4 |
| 8 | 5 |
| 9 | 6 |

Ratios:
- 3/6 = 0.5
- 4/7 ≈ 0.571
- 5/8 = 0.625
- 6/9 ≈ 0.666

→ Not constant → Not proportional

✔ Answer: No

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5) Table 5

| X | Y |
|----|-----|
| 1 | 10 |
| 2 | 20 |
| 7 | 70 |
| 10 | 100 |

Ratios:
- 10/1 = 10
- 20/2 = 10
- 70/7 = 10
- 100/10 = 10

→ All ratios = 10 → Proportional

✔ Answer: Yes

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6) Table 6

| X | Y |
|---|---|
| 2 | 2 |
| 4 | 4 |
| 8 | 8 |
| 10| 10|

Ratios:
- 2/2 = 1
- 4/4 = 1
- 8/8 = 1
- 10/10 = 1

→ Constant ratio = 1 → Proportional

✔ Answer: Yes

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7) Table 7

| X | Y |
|----|-----|
| 20 | -32 |
| 15 | -24 |
| 10 | -16 |
| 5 | -8 |

Ratios:
- -32/20 = -1.6
- -24/15 = -1.6
- -16/10 = -1.6
- -8/5 = -1.6

→ Constant ratio = -1.6 → Proportional

✔ Answer: Yes

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8) Table 8

| X | Y |
|----|-----|
| 70 | -10 |
| 63 | -9 |
| 35 | -5 |
| 21 | -3 |

Ratios:
- -10/70 ≈ -0.1429
- -9/63 ≈ -0.1429
- -5/35 ≈ -0.1429
- -3/21 ≈ -0.1429

→ All ≈ -1/7 → Constant → Proportional

✔ Answer: Yes

---

9) Table 9

| X | Y |
|----|----|
| 2 | 7 |
| 6 | 21 |
| 18 | 63 |
| 20 | 70 |

Ratios:
- 7/2 = 3.5
- 21/6 = 3.5
- 63/18 = 3.5
- 70/20 = 3.5

→ Constant ratio = 3.5 → Proportional

✔ Answer: Yes

---

10) Table 10

| X | Y |
|----|-----|
| -12| -32 |
| -9 | -24 |
| -6 | -16 |
| -3 | -8 |

Ratios:
- -32 / -12 ≈ 2.666...
- -24 / -9 ≈ 2.666...
- -16 / -6 ≈ 2.666...
- -8 / -3 ≈ 2.666...

→ All = 8/3 → Constant → Proportional

✔ Answer: Yes

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11) Table 11

| X | Y |
|----|----|
| 9 | 3 |
| 36 | 6 |
| 64 | 8 |
| 81 | 9 |

Ratios:
- 3/9 = 0.333...
- 6/36 = 0.166...
- 8/64 = 0.125
- 9/81 = 0.111...

→ Not constant → Not proportional

✔ Answer: No

---

12) Table 12

| X | Y |
|---|----|
| 2 | 4 |
| 3 | 6 |
| 4 | 12 |
| 7 | 21 |

Ratios:
- 4/2 = 2
- 6/3 = 2
- 12/4 = 3
- 21/7 = 3

First two: ratio = 2, last two: ratio = 3 → Not constant

✔ Answer: No

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## ✔ Final Answers:

1. No
2. No
3. No
4. No
5. Yes
6. Yes
7. Yes
8. Yes
9. Yes
10. Yes
11. No
12. No

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📌 Summary: Proportionality means Y/X is constant for all pairs. We checked each table and found that tables 5, 6, 7, 8, 9, and 10 are proportional. The rest are not.

You can now fill in the "Answers" column on your worksheet with these results!