Question

Which equation represents a proportional relationship?
Responses

y=−3x+2
y equals negative 3 x plus 2

y = 3x
y = 3 x

y=12x
y equals fraction numerator 1 over denominator 2 x end fraction

y

Answer 1

A proportional relationship can be represented by an equation in the form \( y = kx \), where \( k \) is a constant.

Among the options provided:

1. **y = -3x + 2**: This is not proportional because it has a y-intercept (the constant term +2).
2. **y = 3x**: This is a proportional relationship because it is in the form \( y = kx \) (here, \( k = 3 \)).
3. **y = 12x**: This is also a proportional relationship; it's in the form \( y = kx \) (with \( k = 12 \)).
4. **y = \frac{1}{2} x**: This is another proportional relationship in the form \( y = kx \) (with \( k = \frac{1}{2} \)).

So, the equations that represent a proportional relationship are:

- \( y = 3x \)
- \( y = 12x \)
- \( y = \frac{1}{2} x \)

If you must choose just one, \( y = 3x \) is a clear example of a proportional relationship.