1. The problem asks which equation represents a proportional relationship. 2. A proportional relationship between two variables $x$ and $y$ means $y$ is directly proportional to $x$. 3. The general form of a proportional relationship is: $$y = kx$$ where $k$ is the constant of proportionality. 4. The other equations given are: - $y = k + x$ (not proportional, this is a linear equation with a constant added) - $y = k - x$ (not proportional, linear with subtraction) - $y = \frac{k}{x}$ (inverse proportionality, not direct proportionality) 5. Therefore, the correct equation for a proportional relationship is: $$y = kx$$ This means $y$ changes in direct proportion to $x$ with constant $k$.