Proportional Relationships 8B4F97

1. **State the problem:** We need to classify each given equation as either a proportional relationship or a non-proportional relationship. 2. **Recall the definition:** - A proportional relationship is one where $y$ is directly proportional to $x$, which means the equation can be written as $$y = kx$$ where $k$ is a constant and there is no constant term added or subtracted. - A non-proportional relationship either has an added constant term or is not a linear function of the form $y = kx$. 3. **Analyze each equation:** - $y = \frac{1}{4}x$: This is of the form $y = kx$ with $k=\frac{1}{4}$, so it is proportional. - $y = -6x$: This is of the form $y = kx$ with $k=-6$, so it is proportional. - $y = 2x + 9$: This has an added constant $9$, so it is non-proportional. - $y = \frac{5}{x}$: This is not linear in $x$, so it is non-proportional. - $y = 15x + 3$: This has an added constant $3$, so it is non-proportional. 4. **Summary:** - Proportional: $y = \frac{1}{4}x$, $y = -6x$ - Non-proportional: $y = 2x + 9$, $y = \frac{5}{x}$, $y = 15x + 3$