Question
Which linear equation shows a proportional relationship?
y equals two thirds times x
y equals negative 3 times x minus one seventh
y equals three fourths times x minus 5
y equals 3 times x plus 7
y equals two thirds times x
y equals negative 3 times x minus one seventh
y equals three fourths times x minus 5
y equals 3 times x plus 7
Answers
GPT-4o mini
A linear equation shows a proportional relationship if it can be written in the form \( y = kx \), where \( k \) is a constant. This means that the y-intercept must be zero (the line passes through the origin).
Let's analyze the provided equations:
1. \( y = \frac{2}{3}x \): This is in the form \( y = kx \) with \( k = \frac{2}{3} \). This shows a proportional relationship.
2. \( y = -3x - \frac{1}{7} \): This has a y-intercept of \(-\frac{1}{7}\), so it does not show a proportional relationship.
3. \( y = \frac{3}{4}x - 5 \): This has a y-intercept of \(-5\), so it does not show a proportional relationship.
4. \( y = 3x + 7 \): This has a y-intercept of \(7\), so it does not show a proportional relationship.
The only equation that shows a proportional relationship is:
**\( y = \frac{2}{3}x \)**.
Let's analyze the provided equations:
1. \( y = \frac{2}{3}x \): This is in the form \( y = kx \) with \( k = \frac{2}{3} \). This shows a proportional relationship.
2. \( y = -3x - \frac{1}{7} \): This has a y-intercept of \(-\frac{1}{7}\), so it does not show a proportional relationship.
3. \( y = \frac{3}{4}x - 5 \): This has a y-intercept of \(-5\), so it does not show a proportional relationship.
4. \( y = 3x + 7 \): This has a y-intercept of \(7\), so it does not show a proportional relationship.
The only equation that shows a proportional relationship is:
**\( y = \frac{2}{3}x \)**.