A proportional relationship is one where two quantities maintain a constant ratio. In mathematical terms, a relationship can be expressed as \( y = kx \), where \( k \) is a constant and both \( x \) and \( y \) are directly related by multiplication.
The equation \( y = x + 3 \) does not represent a proportional relationship because it includes an additional constant term (+3). This means that the ratio \( \frac{y}{x} \) is not constant; as \( x \) changes, the value of \( y \) changes in a way that does not maintain a consistent ratio. Specifically, when \( x = 0 \), \( y = 3 \), indicating that when \( x \) is zero, \( y \) does not also equal zero, which is a requirement for proportionality.
Therefore, \( y = x + 3 \) is a linear relationship but not a proportional relationship.