Question

Decide which of the following equations represents a proportional relationship.(1 point)
Responses

y=x+3
y equals x plus 3

y=13x
y equals Start Fraction 1 over 3 End Fraction x

y=x3−3
y equals Start Fraction x over 3 End Fraction minus 3

y=3x+1

Answer 1

A proportional relationship can be represented by an equation of the form \( y = kx \), where \( k \) is a constant and there is no y-intercept other than (0,0).

Let's analyze each of the given equations:

1. **y = x + 3**: This is not a proportional relationship because there is a constant term (+3).

2. **y = 13x**: This is a proportional relationship because it is in the form \( y = kx \) with \( k = 13 \) and passes through the origin (0,0).

3. **y = \frac{x}{3} - 3**: This is not a proportional relationship because of the constant term (-3).

4. **y = 3x + 1**: This is not a proportional relationship because of the constant term (+1).

The only equation that represents a proportional relationship is **y = 13x**.