If y is proportional to x, how can this be expressed mathematically?

When a variable y is said to be proportional to another variable x, it means that y increases or decreases in a consistent ratio to x. This relationship can be expressed mathematically with the formula y = kx, where k is a constant known as the constant of proportionality.

In this equation, k determines how much y changes for a unit change in x, thereby representing the proportionality between the two variables. If you increase x, y increases by the same factor multiplied by k; if you decrease x, y decreases by the same factor multiplied by k.

This direct relationship is pivotal in understanding proportional relationships in various contexts, such as in physics, economics, and everyday situations where one quantity affects another in a predictable manner.

In contrast, the other expressions do not correctly define the relationship where y is directly proportional to x. For example, an additive relationship (like k + x) would indicate that y changes at a fixed amount rather than a fixed ratio, while other forms involving division or reciprocals (like k/x or x/k) do not indicate direct proportionality but rather inverse relationships.