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Determine whether each equation represents a proportional relationship.

1. [tex]\( y = 3 + x \)[/tex]
- Proportional Relationship
- Not a Proportional Relationship

2. [tex]\( y = 1.6x \)[/tex]
- Proportional Relationship
- Not a Proportional Relationship

3. [tex]\( y = \frac{3}{4x} \)[/tex]
- Proportional Relationship
- Not a Proportional Relationship

4. [tex]\( y = x \)[/tex]
- Proportional Relationship
- Not a Proportional Relationship

5. [tex]\( y = 12x \)[/tex]
- Proportional Relationship
- Not a Proportional Relationship

6. [tex]\( y = 2x + 1 \)[/tex]
- Proportional Relationship
- Not a Proportional Relationship

Sagot :

GinnyAnswer
To determine whether each equation represents a proportional relationship, we need to understand what a proportional relationship means. A proportional relationship between two variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex] can be described by an equation of the form [tex]\( y = kx \)[/tex], where [tex]\( k \)[/tex] is a constant.

Let's analyze each equation to see if it fits this form:

1. Equation: [tex]\( y = 3 + x \)[/tex]
- This equation can be rewritten as [tex]\( y = x + 3 \)[/tex], which is not in the form [tex]\( y = kx \)[/tex] because of the additional constant 3.
- Conclusion: Not a Proportional Relationship

2. Equation: [tex]\( y = 1.6x \)[/tex]
- This equation is already in the form [tex]\( y = kx \)[/tex], with [tex]\( k = 1.6 \)[/tex].
- Conclusion: Proportional Relationship

3. Equation: [tex]\( y = \frac{3}{4x} \)[/tex]
- This equation can be written as [tex]\( y = \frac{3}{4} \cdot \frac{1}{x} \)[/tex], which is not in the form [tex]\( y = kx \)[/tex] because of the division by [tex]\( x \)[/tex].
- Conclusion: Not a Proportional Relationship

4. Equation: [tex]\( y = x \)[/tex]
- This equation is already in the form [tex]\( y = kx \)[/tex], with [tex]\( k = 1 \)[/tex].
- Conclusion: Proportional Relationship

5. Equation: [tex]\( y = 12x \)[/tex]
- This equation is already in the form [tex]\( y = kx \)[/tex], with [tex]\( k = 12 \)[/tex].
- Conclusion: Proportional Relationship

6. Equation: [tex]\( y = 2x + 1 \)[/tex]
- This equation can be rewritten as [tex]\( y = 2x + 1 \)[/tex], which is not in the form [tex]\( y = kx \)[/tex] because of the additional constant 1.
- Conclusion: Not a Proportional Relationship

Summarizing, we have:

- [tex]\( y = 3 + x \)[/tex]: Not a Proportional Relationship
- [tex]\( y = 1.6x \)[/tex]: Proportional Relationship
- [tex]\( y = \frac{3}{4x} \)[/tex]: Not a Proportional Relationship
- [tex]\( y = x \)[/tex]: Proportional Relationship
- [tex]\( y = 12x \)[/tex]: Proportional Relationship
- [tex]\( y = 2x + 1 \)[/tex]: Not a Proportional Relationship
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