1. The problem shows a double number line comparing cups of orange juice to cups of grape juice. 2. The top line shows orange juice amounts: 0, 1, 2, 3, 4 cups. 3. The bottom line shows grape juice amounts: 0, 3, 6, 9, 12 cups. 4. We want to find a rate that relates cups of orange juice to cups of grape juice. 5. A rate is a ratio comparing two quantities with different units. 6. From the number line, when orange juice is 1 cup, grape juice is 3 cups. 7. So one rate is $$\frac{\text{3 cups grape juice}}{\text{1 cup orange juice}} = \frac{3}{1}$$. 8. Another way to write this rate is 3 cups of grape juice per 1 cup of orange juice. 9. This means for every cup of orange juice, there are 3 cups of grape juice. 10. You can also write the rate as $$\frac{\text{1 cup orange juice}}{\text{3 cups grape juice}} = \frac{1}{3}$$ if you want the inverse. Final answer: One rate is $$\frac{3}{1}$$ or 3 cups of grape juice per 1 cup of orange juice.