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.