An aquarium needs to hold 9 gal of water for every 3 miniature goldfish. The point on the graph represents this ratio relationship. Which ordered pairs represent equivalent ratios that would also be on the graph? Select all that apply.

To solve this, we first need to understand the ratio of gallons of water to miniature goldfish, which is 9 gallons of water for every 3 goldfish. We can reduce this ratio by dividing both terms by 3:

\[
\frac{9}{3} = 3
\]

So, the ratio of gallons of water to goldfish simplifies to **3 gallons per goldfish**. This is the constant ratio that any equivalent ordered pairs must follow. 

The ordered pairs must represent this same ratio, which means for any number of goldfish \( x \), the number of gallons \( y \) must satisfy the equation:

\[
y = 3x
\]

Now, let's look at which ordered pairs represent equivalent ratios (following the form \( (x, y) \), where \( x \) is the number of goldfish and \( y \) is the number of gallons of water):

- \( (1, 3) \): 1 goldfish, 3 gallons of water → ratio is \( \frac{3}{1} = 3 \) — **Equivalent ratio**.
- \( (2, 6) \): 2 goldfish, 6 gallons of water → ratio is \( \frac{6}{2} = 3 \) — **Equivalent ratio**.
- \( (3, 9) \): 3 goldfish, 9 gallons of water → ratio is \( \frac{9}{3} = 3 \) — **Equivalent ratio**.
- \( (4, 10) \): 4 goldfish, 10 gallons of water → ratio is \( \frac{10}{4} = 2.5 \) — **Not an equivalent ratio**.
- \( (5, 15) \): 5 goldfish, 15 gallons of water → ratio is \( \frac{15}{5} = 3 \) — **Equivalent ratio**.

So, the ordered pairs that represent equivalent ratios are:

- \( (1, 3) \)
- \( (2, 6) \)
- \( (3, 9) \)
- \( (5, 15) \)

### Would you like more details on ratio equivalency or have any questions?

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Here are five questions to further explore this concept:

1. What happens if the number of goldfish increases to 6?
2. How would the equation change if we change the ratio of gallons per fish?
3. What is the significance of reducing a ratio in real-world applications?
4. How can you find an equivalent ratio without reducing it first?
5. How would this ratio change if we added a condition for a different type of fish?

**Tip**: Always simplify ratios when possible to make comparisons easier!

Learn how to identify equivalent ratios in the context of an aquarium needing 9 gallons of water for every 3 miniature goldfish. This problem explores proportional relationships and how to determine which ordered pairs, such as (1, 3) and (2, 6), meet the same ratio criteria. Ideal for students in Grades 6-8.

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