https://file.aiquickdraw.com/mathbot/file/1725993248125evnjj094.jpg

The graph in the image shows a line that represents a proportional relationship. To match the proportional relationship to a scenario, let's first determine the slope of the line.

### Step 1: Analyzing the Graph
- The graph has the line passing through the origin $(0, 0)$, which is characteristic of proportional relationships.
- From visual inspection, the line appears to pass through points like $(5, 3)$, meaning for every 5 units increase on the x-axis, there is a 3-unit increase on the y-axis. This gives a slope (rate of change) of $ \frac{3}{5} $, or 3 cakes per 5 days.

### Step 2: Comparing to the Given Scenarios
Now, let's compare this rate to the options provided:
- **A:** "A chef bakes 3 cakes every 5 days."  
  This matches the slope we calculated from the graph: $ \frac{3}{5} $.
  
- **B:** "Michael paid $25 for 4 hamburgers."  
  The rate here would be $ \frac{25}{4} $, which does not match the graph's slope.
  
- **C:** "Gail can buy 5 pencils for $10 at the school store."  
  This gives a rate of $ \frac{5}{10} = \frac{1}{2} $, which is also different from the graph.
  
- **D:** "Every 14 days, a worker deposits $25 into a savings account."  
  This gives a rate of $ \frac{25}{14} $, which is not the same as the graph's slope.

### Conclusion:
The correct answer is **A: A chef bakes 3 cakes every 5 days** because it directly matches the slope of the line on the graph, which is $ \frac{3}{5} $.

Would you like more details on any step? Here are some additional questions to consider:

1. What are proportional relationships and how are they represented graphically?
2. How do you calculate the slope of a line on a graph?
3. Why do proportional relationships always pass through the origin?
4. How do you compare different rates of change in word problems?
5. Can a graph of a proportional relationship ever have a curve?

**Tip:** When analyzing proportional relationships, always look for the constant rate of change, or slope, which is the same between any two points on the line.

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

Analyze a proportional relationship represented on a graph and match it to real-world scenarios. This problem covers key concepts like slope, rate of change, and proportionality, ideal for Grades 6-8.

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