Final answer:
An equation that represents the proportional relationship between oil and vinegar can be written as O = kV, where O is the amount of oil, V is the amount of vinegar, and k is the constant of proportionality representing the ratio of oil to vinegar.
Step-by-step explanation:
To write an equation that represents the proportional relationship between oil and vinegar, we need to choose variables to represent the quantities of each. Let's let O represent the amount of oil and V represent the amount of vinegar. A simple equation that maintains a proportional relationship is O = kV, where k is the constant of proportionality. This constant represents the ratio of oil to vinegar in the mixture. For example, if a salad dressing recipe calls for oil and vinegar in a 2:1 ratio, then k would be equal to 2.
If we rearrange the equation to solve for V, we get V = O/k, which means that the amount of vinegar is inversely proportional to the constant k when the amount of oil O is held constant. This illustrates the concept of inverse proportionality.
To further understand this proportional relationship, consider if the recipe requires 4 tablespoons of oil; with a ratio of 2:1, you would need 2 tablespoons of vinegar. Using the proportional equation, if O = 4 tablespoons and k = 2, then V = 4/2, so V = 2 tablespoons. This highlights how changes in one variable affect the other in a consistent and predictable way based on the constant k.