### Exploring Proportional Relationships Consider the following table. Is the relationship proportional? Explain your answer by examining the values in the table.| x | y ||:----:|:-----:|| -2 | -27 || 1 | 12 || 4 | 57 || 10 | 147 |#### AnalysisTo determine if the relationship between $ x $ and $ y $ is proportional, we need to check if the ratio $ \frac{y}{x} $ is constant across all pairs of values. This means the ratio should be the same for every pair $(x, y)$.#### Calculations1. Calculate the ratio for each pair: - For $ x = -2 $ and $ y = -27 $: $ \frac{-27}{-2} = 13.5 $ - For $ x = 1 $ and $ y = 12 $: $ \frac{12}{1} = 12 $ - For $ x = 4 $ and $ y = 57 $: $ \frac{57}{4} = 14.25 $ - For $ x = 10 $ and $ y = 147 $: $ \frac{147}{10} = 14.7 $Since the ratios are not the same, the relationship is not proportional.#### ConclusionThe relationship between $ x $ and $ y $ is not proportional because the ratio of $ y $ to $ x $ is not constant across the table.

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Description: ### Exploring Proportional Relationships Consider the following table. Is the relationship proportional? Explain your answer by examining the values in the table.| x | y ||:----:|:-----:|| -2 | -27 || 1 | 12 || 4 | 57 || 10

We have to define relationship is proportional or not

Answered: Consider the following table. Is the…

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Consider the following table. Is the relationship proportional? Explain your answer. y -2 -27 1 12 4 57 10 147

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### Exploring Proportional Relationships

Consider the following table. Is the relationship proportional? Explain your answer by examining the values in the table.

| x | y |
|:----:|:-----:|
| -2 | -27 |
| 1 | 12 |
| 4 | 57 |
| 10 | 147 |

#### Analysis

To determine if the relationship between $ x $ and $ y $ is proportional, we need to check if the ratio $ \frac{y}{x} $ is constant across all pairs of values. This means the ratio should be the same for every pair $(x, y)$.

#### Calculations
1. Calculate the ratio for each pair:
- For $ x = -2 $ and $ y = -27 $: $ \frac{-27}{-2} = 13.5 $
- For $ x = 1 $ and $ y = 12 $: $ \frac{12}{1} = 12 $
- For $ x = 4 $ and $ y = 57 $: $ \frac{57}{4} = 14.25 $
- For $ x = 10 $ and $ y = 147 $: $ \frac{147}{10} = 14.7 $

Since the ratios are not the same, the relationship is not proportional.

#### Conclusion

The relationship between $ x $ and $ y $ is not proportional because the ratio of $ y $ to $ x $ is not constant across the table.

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