Question
Decide which of the following equations represents a proportional relationship.(1 point) Responses y=3x+1 y equals 3 x plus 1 y=x+3 y equals x plus 3 y=13x y equals Start Fraction 1 over 3 End Fraction x y=x3−3
Answers
Answered by
GPT-4o mini
A proportional relationship between two variables can be represented by the equation \( y = kx \), where \( k \) is a constant. This means that the relationship has a constant ratio between \( y \) and \( x \), and it passes through the origin (0,0).
Let's analyze each of the provided equations:
1. **\( y = 3x + 1 \)**: This is not proportional because it has a constant term (1), so it does not pass through the origin.
2. **\( y = x + 3 \)**: This is also not proportional, as it has a constant term (3) and does not pass through the origin.
3. **\( y = 13x \)**: This is proportional because it has the form \( y = kx \) with \( k = 13 \) and passes through the origin.
4. **\( y = \frac{1}{3}x \)**: This is proportional because it also has the form \( y = kx \) with \( k = \frac{1}{3} \) and passes through the origin.
5. **\( y = x^3 - 3 \)**: This is not proportional because it has a constant term (-3) and does not pass through the origin.
The equations that represent proportional relationships are \( y = 13x \) and \( y = \frac{1}{3}x \).
Let's analyze each of the provided equations:
1. **\( y = 3x + 1 \)**: This is not proportional because it has a constant term (1), so it does not pass through the origin.
2. **\( y = x + 3 \)**: This is also not proportional, as it has a constant term (3) and does not pass through the origin.
3. **\( y = 13x \)**: This is proportional because it has the form \( y = kx \) with \( k = 13 \) and passes through the origin.
4. **\( y = \frac{1}{3}x \)**: This is proportional because it also has the form \( y = kx \) with \( k = \frac{1}{3} \) and passes through the origin.
5. **\( y = x^3 - 3 \)**: This is not proportional because it has a constant term (-3) and does not pass through the origin.
The equations that represent proportional relationships are \( y = 13x \) and \( y = \frac{1}{3}x \).