Question

Decide which of the following equations represents a proportional relationship?
y=1/3x
y=x/3 - 3
y= 3x+1
y= x +3

Answer 1

A proportional relationship can be represented by an equation of the form \( y = kx \), where \( k \) is a constant. This means that the relationship goes through the origin (0,0) and does not include any constant term added or subtracted from the equation.

Let's analyze the given equations one by one:

1. **\( y = \frac{1}{3}x \)**: This is in the form \( y = kx \) where \( k = \frac{1}{3} \). This represents a proportional relationship because it goes through the origin.

2. **\( y = \frac{x}{3} - 3 \)**: This equation has a constant term (-3) added, so it does not pass through the origin. Therefore, it does not represent a proportional relationship.

3. **\( y = 3x + 1 \)**: This equation also has a constant term (+1) added, meaning it does not pass through the origin. Thus, it does not represent a proportional relationship.

4. **\( y = x + 3 \)**: Similarly, this equation has a constant term (+3) added and does not pass through the origin, so it does not represent a proportional relationship.

The only equation that represents a proportional relationship is:

**\( y = \frac{1}{3}x \)**.