Answered

Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

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
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.