https://r2.erweima.ai/mathbot/image/172599299544903lq793s.jpg

The graph in the image represents a proportional relationship. To find the correct scenario that matches the relationship shown, we need to determine the constant rate of change or unit rate.

### Analysis of the Graph:
The graph shows a straight line that passes through the origin (0,0), which confirms a proportional relationship. From the graph, let's identify the points that the line passes through. We see that at $x = 1$, $y = 10$; at $x = 2$, $y = 20$; and so on. This suggests that for every 1 unit increase in $x$, $y$ increases by 10.

So, the unit rate is $ y = 10x $, meaning that for each unit increase in $x$, $y$ increases by 10.

### Comparing the Scenarios:

A) **Aaron spent $30 to buy 3 DVDs.**
   - This scenario suggests a rate of $ \frac{30}{3} = 10 $, which means Aaron spends $10 per DVD. This matches the unit rate from the graph.

B) **Dakota earns $15 for each dog she walks.**
   - The unit rate here is $15 per dog, which doesn't match the rate of 10 from the graph.

C) **A customer can buy 5 exotic fish for $30 at a pet shop.**
   - This suggests a rate of $ \frac{30}{5} = 6 $, which doesn't match the rate of 10 from the graph.

D) **A student can complete 2 math assignments in 60 minutes.**
   - This suggests a rate of $ \frac{60}{2} = 30 $ minutes per assignment, which doesn't match the rate of 10 from the graph.

### Conclusion:
The scenario that best matches the proportional relationship shown on the graph is **A) Aaron spent $30 to buy 3 DVDs**, since the unit rate matches the graph's rate of $10 per DVD.

Would you like further clarification or have any more questions? Here are some related questions you might find helpful:

1. How can you find the constant of proportionality from a table of values?
2. What are other real-life examples of proportional relationships?
3. What changes to the graph would indicate a non-proportional relationship?
4. How would the graph look if the unit rate was 5 instead of 10?
5. How do you calculate the slope of a proportional relationship?

**Tip:** In a proportional relationship, the graph will always pass through the origin, and the ratio between $ y $ and $ x $ will always remain constant.

Which scenario best matches the proportional relationship shown on the graph?

Explore how to interpret proportional relationships from a graph. This problem involves determining the unit rate and identifying the best matching real-life scenario, suitable for students in Grades 6-8.

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