Proportions Worksheets - Free Printable

Since I can't view or access uploaded images directly, I can't see the specific content of your image. However, based on your description — "Properties - Table" and the mention of determining whether the *add* and *subtract* rules in each table are proportional — I can help you solve this type of problem.

Let me walk you through how to analyze such a task in general, and then you can apply it to your tables.

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🔍 Objective:

Determine whether the add and subtract rules in each table are proportional.

> A relationship is proportional if:
> - It can be written as $ y = kx $ (no constant term added/subtracted).
> - The ratio $ \frac{y}{x} $ is constant for all pairs.
> - The graph passes through the origin (0,0) — but since we're dealing with tables, we check ratios.

Also, note:
- Add rule: means $ y = x + c $
- Subtract rule: means $ y = x - c $
- These are not proportional unless $ c = 0 $, because they include a constant shift.

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✔ How to Check Proportionality:

For each table:

1. Check if the ratio $ \frac{y}{x} $ is constant across all rows.
- If yes → proportional.
- If not → not proportional.

2. Check if there's a pattern like “add” or “subtract”:
- If $ y = x + c $ or $ y = x - c $, that’s not proportional unless $ c = 0 $.
- But if $ y = kx $, where $ k $ is a constant multiplier, then it is proportional.

3. Look for a multiplicative relationship:
- Is each $ y $ a multiple of $ x $? For example: $ y = 2x $, $ y = 3x $, etc.

4. Check if $ x = 0 $ leads to $ y = 0 $:
- In a proportional relationship, when $ x = 0 $, $ y $ must also be 0.

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🧩 Example Walkthrough

Suppose one table looks like this:

| x | y |
|---|---|
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |

- $ y/x $: 3/1 = 3, 6/2 = 3, 9/3 = 3 → constant ratio
- So, $ y = 3x $ → proportional

Now suppose another:

| x | y |
|---|---|
| 1 | 4 |
| 2 | 5 |
| 3 | 6 |

- $ y/x $: 4/1 = 4, 5/2 = 2.5, 6/3 = 2 → not constant
- Also, $ y = x + 3 $ → add rule, so not proportional

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📌 Summary Rule:

| Rule Type | Proportional? | Why? |
|------------------|---------------|------|
| $ y = kx $ | ✔ Yes | Constant ratio, goes through origin |
| $ y = x + c $ | ✘ No | Additive constant → not proportional |
| $ y = x - c $ | ✘ No | Same reason |
| $ y = kx + b $ | ✘ No | Unless $ b = 0 $ |

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🔁 Apply This to Your Tables

Now, go through each of the six tables in your worksheet:

For each table:
1. Compute $ y/x $ for each row.
2. If all ratios are equal → proportional.
3. If not → not proportional.
4. Also, check if the rule is clearly additive (like adding 3 every time), which would mean not proportional.

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💡 Final Tips:

- Look for patterns: Is $ y $ always double $ x $? Triple? That’s proportional.
- If $ y $ increases by a fixed amount while $ x $ increases by 1 → that’s linear, but not necessarily proportional.
- Only if it passes through (0,0) AND has constant ratio → proportional.

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If you can describe or list the values from each table (e.g., “Table 1: x=2,y=6; x=4,y=12; x=6,y=18”), I can help you determine proportionality for each one.

Let me know!