Direct Variation and Inverse Variation Worksheets - Free Printable

It looks like you're referring to a worksheet titled "Direct and Inverse Variation: Table", which asks students to determine whether each table represents a direct variation, an inverse variation, or neither. The goal is to analyze the relationship between two variables (x and y) in each table.

Since I can't view images directly, I’ll guide you through how to solve this type of problem step by step. If you can provide the actual numbers from the tables (or describe them), I can help you solve it specifically.

But here’s how to approach it:

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🔍 Step-by-Step Guide:

#### ✔ Direct Variation
A direct variation means:
- $ y = kx $, where $ k $ is a constant.
- As $ x $ increases, $ y $ increases proportionally.
- The ratio $ \frac{y}{x} $ is constant for all pairs.

👉 Check: Is $ \frac{y}{x} $ the same for every row?

#### ✔ Inverse Variation
An inverse variation means:
- $ y = \frac{k}{x} $, so $ xy = k $, where $ k $ is constant.
- As $ x $ increases, $ y $ decreases.
- The product $ x \cdot y $ is constant for all pairs.

👉 Check: Is $ x \cdot y $ the same for every row?

#### ✘ Neither
If neither the ratio $ \frac{y}{x} $ nor the product $ x \cdot y $ is constant, then it's neither.

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🧩 Example Analysis (Hypothetical)

Let’s say one table has:

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

Check $ \frac{y}{x} $:
- $ 3/1 = 3 $
- $ 6/2 = 3 $
- $ 9/3 = 3 $

✔ Constant → Direct Variation

Another table:

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

Check $ x \cdot y $:
- $ 1×6 = 6 $
- $ 2×3 = 6 $
- $ 3×2 = 6 $

✔ Constant → Inverse Variation

Another:

| x | y |
|---|---|
| 1 | 2 |
| 2 | 5 |
| 3 | 8 |

$ y/x $: 2, 2.5, 2.67 → not constant
$ x·y $: 2, 10, 24 → not constant

✘ Neither

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📝 Instructions for You:

Please provide the data from the four tables in your image (you can copy-paste the values or list them). For example:

> Table 1:
> x: 1, 2, 3, 4
> y: 4, 8, 12, 16

Then I can tell you whether each is direct, inverse, or neither — and explain why.

Once you give me the numbers, I’ll solve it fully!