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The table shows the relationship between the number of miles traveled, \( x \), and the number of gallons of gas used, \( y \). The pattern in the table suggests a proportional relationship between \( x \) and \( y \). 

Looking at the values:
- When \( x = 35 \), \( y = 1 \)
- When \( x = 70 \), \( y = 2 \)
- When \( x = 105 \), \( y = 3 \)
- When \( x = 140 \), \( y = 4 \)
- When \( x = 175 \), \( y = 5 \)

This suggests that \( x \) increases by 35 for every increase of 1 in \( y \), indicating a direct proportionality: \( y \propto x \). Specifically, the relationship is:

\[
y = \frac{x}{35} \quad \text{or equivalently,} \quad x = 35y
\]

Therefore, the best equation to represent this relationship is:
\[
y = \frac{x}{35} \quad \text{or} \quad y = \frac{1}{35}x
\]

However, the correct equation marked in the answer is **\( y = 35x \)**, which is incorrect based on the table values, as it should be \( y = \frac{1}{35}x \).

Would you like a detailed explanation of this reasoning? Here are five additional questions you can explore:

1. How do you derive equations from proportional relationships?
2. How can you graph this relationship between \( x \) and \( y \)?
3. What is the slope in this context, and how does it affect the equation?
4. Can you explain why \( y = 35x \) doesn't fit this scenario?
5. How does unit rate impact real-world problems like this?

**Tip:** When working with proportional relationships, always check if the pattern is increasing or decreasing at a constant rate, as this will guide you to the correct linear equation.

The table shows the relationship between the number of miles traveled, x, and the number of gallons of gas used, y. Which equation best represents the relationship?

Learn how to solve a proportional relationship problem between miles traveled and gallons of gas used. Given a table showing the values, this example demonstrates the best equation to represent the relationship as y = 35x.

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