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The problem presents a graph showing the relationship between Australian dollars (AUD) and American dollars (USD). The task is to write an equation representing the relationship, where \( y \) is the amount in AUD, and \( x \) is the amount in USD.

### Step-by-Step Analysis:

1. **Identify the linear nature of the graph**: The graph shows a straight line, indicating a linear relationship between AUD and USD. The equation should follow the form:
   \[
   y = mx + b
   \]
   where \( m \) is the slope, and \( b \) is the y-intercept.

2. **Determine the slope**: The slope \( m \) can be calculated by finding the ratio of the change in AUD to the change in USD. From the graph:
   - At \( x = 0 \) USD, \( y = 0 \) AUD (this suggests \( b = 0 \), as the line passes through the origin).
   - At \( x = 700 \) USD, \( y = 700 \) AUD.

   The slope \( m \) is:
   \[
   m = \frac{\Delta y}{\Delta x} = \frac{700 - 0}{700 - 0} = 1
   \]

3. **Equation**: Since the slope \( m = 1 \) and the y-intercept \( b = 0 \), the equation becomes:
   \[
   y = x
   \]

Thus, the relationship between AUD and USD is simply \( y = x \), meaning that 1 AUD is equivalent to 1 USD according to this graph at that specific time.

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Would you like further clarification or more details on any part of this solution?

Here are five related questions to extend your understanding:
1. What would happen to the equation if the line didn't pass through the origin?
2. How would the equation change if 1 AUD equaled 0.75 USD?
3. Can you describe how to interpret the slope of the line in this context?
4. What is the significance of the y-intercept in currency conversion graphs?
5. How would you graph a scenario where 1 AUD is worth more than 1 USD?

**Tip**: In linear graphs representing exchange rates, the slope represents the exchange rate between the two currencies!

The graph shows the equivalent value of Australian dollars (AUD) and American dollars (USD) at a specific time in the past. Write an equation representing the relationship between the two currencies, where y is Australian dollars and x is American dollars.

Analyze the graph showing the equivalent value of Australian dollars (AUD) and American dollars (USD) and learn how to derive a linear equation y = mx + b representing the relationship between the two currencies. Suitable for Grades 8-10.

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