Which of the following equations represent a proportional relationship? Circle all that apply.

To determine which equations represent a proportional relationship, we need to identify equations that can be expressed in the form \( y = kx \), where \( k \) is a constant. A proportional relationship means that as one quantity changes, the other quantity changes at a constant rate, and the graph of the relationship passes through the origin (0,0). Here are some common forms of equations to consider: 1. **Linear equations of the form \( y = mx + b \)**: If \( b = 0 \), then it represents a proportional relationship. If \( b \neq 0 \), it does not. 2. **Equations of the form \( y = kx \)**: These represent proportional relationships. 3. **Equations that can be simplified to the form \( y = kx \)**: If you can manipulate the equation to get it into this form, it represents a proportional relationship. 4. **Equations that include a constant term or do not pass through the origin**: These do not represent proportional relationships. If you provide the specific equations you want to analyze, I can help you determine which ones represent a proportional relationship.