Question
Do the data in the table represent a direct variation or an inverse variation? Write an equation to model the data in the table.
direct variation; y = 12x
inverse variation; xy = 12
direct variation; y = 12x
inverse variation; xy = 12
Answers
GPT-4o mini
To determine whether the data represents a direct variation or an inverse variation, let's clarify the definitions:
- **Direct Variation**: This type of variation means that \(y\) is directly proportional to \(x\). The relationship can be expressed as \(y = kx\), where \(k\) is a constant.
- **Inverse Variation**: In this case, \(y\) is inversely proportional to \(x\), and it can be expressed as \(xy = k\) or \(y = \frac{k}{x}\), where \(k\) is a constant.
From your question, you provided two equations:
1. **Direct Variation**: \(y = 12x\)
2. **Inverse Variation**: \(xy = 12\)
If you have specific data points in a table, you would evaluate the relationship between \(x\) and \(y\) to see if they fit one of these forms:
- For direct variation, if you can express \(y\) as a constant multiplied by \(x\), then it shows direct variation.
- For inverse variation, if the product of \(x\) and \(y\) remains constant and equals a fixed value (like 12 in your case), then it shows inverse variation.
Based on what you've provided:
1. The equation \(y = 12x\) suggests a direct variation where \(k = 12\).
2. The equation \(xy = 12\) suggests an inverse variation where \(k = 12\).
If you have data that fits one of these relationships, you would determine the nature of the variation based on how the \(x\) and \(y\) values relate.
If you're given a specific set of values, please share them to clarify whether they represent direct or inverse variation based on the calculations. If they satisfy both conditions, you might need to clarify which equation is fitting better for your context.
- **Direct Variation**: This type of variation means that \(y\) is directly proportional to \(x\). The relationship can be expressed as \(y = kx\), where \(k\) is a constant.
- **Inverse Variation**: In this case, \(y\) is inversely proportional to \(x\), and it can be expressed as \(xy = k\) or \(y = \frac{k}{x}\), where \(k\) is a constant.
From your question, you provided two equations:
1. **Direct Variation**: \(y = 12x\)
2. **Inverse Variation**: \(xy = 12\)
If you have specific data points in a table, you would evaluate the relationship between \(x\) and \(y\) to see if they fit one of these forms:
- For direct variation, if you can express \(y\) as a constant multiplied by \(x\), then it shows direct variation.
- For inverse variation, if the product of \(x\) and \(y\) remains constant and equals a fixed value (like 12 in your case), then it shows inverse variation.
Based on what you've provided:
1. The equation \(y = 12x\) suggests a direct variation where \(k = 12\).
2. The equation \(xy = 12\) suggests an inverse variation where \(k = 12\).
If you have data that fits one of these relationships, you would determine the nature of the variation based on how the \(x\) and \(y\) values relate.
If you're given a specific set of values, please share them to clarify whether they represent direct or inverse variation based on the calculations. If they satisfy both conditions, you might need to clarify which equation is fitting better for your context.