1. **Stating the problem:** We are given points on a graph representing Corey’s earnings over weeks worked. We need to determine which statements about these points correctly describe the situation. 2. **Understanding the graph:** The graph shows a proportional relationship between weeks worked ($x$) and money earned ($y$). The line passes through $(0,0)$ and $(5,1000)$, indicating Corey earns money at a constant rate. 3. **Formula for proportional relationship:** $$y = kx$$ where $k$ is the constant rate of earnings per week. 4. **Find $k$ using the point $(5,1000)$:** $$1000 = k \times 5$$ $$k = \frac{1000}{5} = 200$$ 5. **Interpretation:** Corey earns $200 each week. 6. **Check each statement:** - A. $(0,0)$ means at 0 weeks, Corey has earned 0 money. This is true. - B. $(1,100)$ means Corey earns 100 each week. This is false because $k=200$. - C. $(1,200)$ means Corey earns 200 each week. This is true. - D. $(2,300)$ means Corey has earned 300 after 2 weeks. This is false because $2 \times 200 = 400$. - E. $(4,800)$ means Corey has earned 800 after 4 weeks. This is true because $4 \times 200 = 800$. **Final correct statements:** A, C, and E.