Question
What would show a proportional relationship between x and y
Answers
Answered by
GPT-4o mini
A proportional relationship between two variables, \( x \) and \( y \), can be expressed with the equation:
\[
y = kx
\]
where \( k \) is a constant known as the constant of proportionality. In such a relationship:
1. **Directly Proportional:** If \( x \) increases, \( y \) increases proportionally, and if \( x \) decreases, \( y \) decreases proportionally.
2. **Graphically:** The graph of a proportional relationship is a straight line that passes through the origin (0,0). The slope of the line represents the constant \( k \).
3. **Ratios:** The ratio \( \frac{y}{x} \) remains constant for all pairs of \( (x, y) \). In other words, if you take any two points on the line, the ratio of their \( y \)-values to their corresponding \( x \)-values should be the same.
4. **Data Table:** If you compile a table of values for \( x \) and \( y \), the values should reflect a consistent ratio. For instance, if every time \( x \) doubles, \( y \) should also double.
5. **Examples:** Some classic examples of proportional relationships include:
- The distance traveled at a constant speed (distance = speed × time).
- The cost of items at a constant price (cost = price per item × number of items).
If these conditions are met, then you can confidently say that \( x \) and \( y \) exhibit a proportional relationship.
\[
y = kx
\]
where \( k \) is a constant known as the constant of proportionality. In such a relationship:
1. **Directly Proportional:** If \( x \) increases, \( y \) increases proportionally, and if \( x \) decreases, \( y \) decreases proportionally.
2. **Graphically:** The graph of a proportional relationship is a straight line that passes through the origin (0,0). The slope of the line represents the constant \( k \).
3. **Ratios:** The ratio \( \frac{y}{x} \) remains constant for all pairs of \( (x, y) \). In other words, if you take any two points on the line, the ratio of their \( y \)-values to their corresponding \( x \)-values should be the same.
4. **Data Table:** If you compile a table of values for \( x \) and \( y \), the values should reflect a consistent ratio. For instance, if every time \( x \) doubles, \( y \) should also double.
5. **Examples:** Some classic examples of proportional relationships include:
- The distance traveled at a constant speed (distance = speed × time).
- The cost of items at a constant price (cost = price per item × number of items).
If these conditions are met, then you can confidently say that \( x \) and \( y \) exhibit a proportional relationship.
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