Asked by botfor1
Write the equation of the line y=mx through the origin that describes the proportional relationship
A.
y = 1/2x
B.
y = x
C.
y = 2x
A.
y = 1/2x
B.
y = x
C.
y = 2x
Answers
Answered by
GPT-4o mini
The equation of a line in the form \( y = mx \) describes a proportional relationship through the origin, where \( m \) is the slope of the line.
1. **Option A:** \( y = \frac{1}{2}x \) has a slope of \( \frac{1}{2} \).
2. **Option B:** \( y = x \) has a slope of \( 1 \).
3. **Option C:** \( y = 2x \) has a slope of \( 2 \).
All three options describe lines through the origin and represent proportional relationships.
To summarize:
- \( y = \frac{1}{2}x \) reflects a lower proportionality to \( x \).
- \( y = x \) reflects a one-to-one proportionality to \( x \).
- \( y = 2x \) reflects a greater proportionality than \( x \).
Thus, all three equations \( y = \frac{1}{2}x \), \( y = x \), and \( y = 2x \) are valid equations for lines that describe proportional relationships through the origin.
1. **Option A:** \( y = \frac{1}{2}x \) has a slope of \( \frac{1}{2} \).
2. **Option B:** \( y = x \) has a slope of \( 1 \).
3. **Option C:** \( y = 2x \) has a slope of \( 2 \).
All three options describe lines through the origin and represent proportional relationships.
To summarize:
- \( y = \frac{1}{2}x \) reflects a lower proportionality to \( x \).
- \( y = x \) reflects a one-to-one proportionality to \( x \).
- \( y = 2x \) reflects a greater proportionality than \( x \).
Thus, all three equations \( y = \frac{1}{2}x \), \( y = x \), and \( y = 2x \) are valid equations for lines that describe proportional relationships through the origin.