1. The problem asks which equation does NOT represent a linear proportional relationship. 2. A linear proportional relationship has the form $y = kx$, where $k$ is a constant and the graph passes through the origin $(0,0)$. 3. Let's analyze each option: - A: $y = -4x$ is of the form $y = kx$ with $k = -4$, so it is proportional. - B: $y = \frac{4}{7}x$ is of the form $y = kx$ with $k = \frac{4}{7}$, so it is proportional. - C: $y = \frac{12x}{5}$ can be rewritten as $y = \left(\frac{12}{5}\right)x$, so it is proportional. - D: $y = x - 3$ can be rewritten as $y = 1 \cdot x - 3$. This is a linear equation but not proportional because of the $-3$ (y-intercept not zero). 4. Therefore, the equation that does NOT represent a linear proportional relationship is option D. **Final answer:** $y = x - 3$ (Option D)