Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
Roni wants to write an equation to represent a proportional relationship that has a constant of proportionality equal to [tex]\(\frac{7}{25}\)[/tex]. She writes the equation [tex]\(y = x + \frac{7}{25}\)[/tex].
Let's analyze the problem step-by-step:
1. Understanding Proportional Relationships:
- A proportional relationship between two variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex] means that as [tex]\(x\)[/tex] changes, [tex]\(y\)[/tex] changes in such a way that their ratio remains constant. This can be represented as [tex]\(y = kx\)[/tex], where [tex]\(k\)[/tex] is the constant of proportionality.
2. Constant of Proportionality:
- In this case, the constant of proportionality is given as [tex]\(\frac{7}{25}\)[/tex]. Therefore, the correct equation representing this relationship should be [tex]\(y = \frac{7}{25} x\)[/tex].
3. Analyzing Roni's Equation:
- Roni wrote the equation as [tex]\(y = x + \frac{7}{25}\)[/tex]. This equation represents a linear relationship, but it is not a proportional relationship because it includes an additive term [tex]\(\frac{7}{25}\)[/tex] instead of a multiplicative constant.
4. Matching the Options:
- The first incorrect option proposes [tex]\(y = -x + \frac{7}{25}\)[/tex], suggesting a different type of relationship where [tex]\(y\)[/tex] has a constant sum with [tex]\(x\)[/tex]. This is not relevant to a proportional relationship.
- The second incorrect option proposes [tex]\(xy = \frac{7}{25}\)[/tex], indicating a relationship where [tex]\(x\)[/tex] and [tex]\(y\)[/tex] have a constant product. This does not describe the proportional relationship in question.
- The correct option proposes [tex]\(y = \frac{7}{25} x\)[/tex], which matches the definition of a proportional relationship with a constant of proportionality [tex]\(\frac{7}{25}\)[/tex]. This correctly ensures that the ratio [tex]\(y/x\)[/tex] remains constant at [tex]\(\frac{7}{25}\)[/tex].
- The fourth incorrect option suggests [tex]\(y = \frac{7}{25}\)[/tex], which indicates that [tex]\(y\)[/tex] is constant for all values of [tex]\(x\)[/tex]. This does not correctly describe a proportional relationship.
Based on the analysis, the error Roni is making is that she wrote the equation as [tex]\(y = x + \frac{7}{25}\)[/tex] instead of the correct form for a proportional relationship, which should be [tex]\(y = \frac{7}{25} x\)[/tex]. Therefore, the right choice is:
She should have written [tex]\(y = \frac{7}{25} x\)[/tex] so that [tex]\(x\)[/tex] and [tex]\(y\)[/tex] have a constant quotient.
Let's analyze the problem step-by-step:
1. Understanding Proportional Relationships:
- A proportional relationship between two variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex] means that as [tex]\(x\)[/tex] changes, [tex]\(y\)[/tex] changes in such a way that their ratio remains constant. This can be represented as [tex]\(y = kx\)[/tex], where [tex]\(k\)[/tex] is the constant of proportionality.
2. Constant of Proportionality:
- In this case, the constant of proportionality is given as [tex]\(\frac{7}{25}\)[/tex]. Therefore, the correct equation representing this relationship should be [tex]\(y = \frac{7}{25} x\)[/tex].
3. Analyzing Roni's Equation:
- Roni wrote the equation as [tex]\(y = x + \frac{7}{25}\)[/tex]. This equation represents a linear relationship, but it is not a proportional relationship because it includes an additive term [tex]\(\frac{7}{25}\)[/tex] instead of a multiplicative constant.
4. Matching the Options:
- The first incorrect option proposes [tex]\(y = -x + \frac{7}{25}\)[/tex], suggesting a different type of relationship where [tex]\(y\)[/tex] has a constant sum with [tex]\(x\)[/tex]. This is not relevant to a proportional relationship.
- The second incorrect option proposes [tex]\(xy = \frac{7}{25}\)[/tex], indicating a relationship where [tex]\(x\)[/tex] and [tex]\(y\)[/tex] have a constant product. This does not describe the proportional relationship in question.
- The correct option proposes [tex]\(y = \frac{7}{25} x\)[/tex], which matches the definition of a proportional relationship with a constant of proportionality [tex]\(\frac{7}{25}\)[/tex]. This correctly ensures that the ratio [tex]\(y/x\)[/tex] remains constant at [tex]\(\frac{7}{25}\)[/tex].
- The fourth incorrect option suggests [tex]\(y = \frac{7}{25}\)[/tex], which indicates that [tex]\(y\)[/tex] is constant for all values of [tex]\(x\)[/tex]. This does not correctly describe a proportional relationship.
Based on the analysis, the error Roni is making is that she wrote the equation as [tex]\(y = x + \frac{7}{25}\)[/tex] instead of the correct form for a proportional relationship, which should be [tex]\(y = \frac{7}{25} x\)[/tex]. Therefore, the right choice is:
She should have written [tex]\(y = \frac{7}{25} x\)[/tex] so that [tex]\(x\)[/tex] and [tex]\(y\)[/tex] have a constant quotient.
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
