Question

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

y=x+3
y equals x plus 3

y=3x+1
y equals 3 x plus 1

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

y=x3−3

Answer 1

A proportional relationship can be identified through the general form of the equation \(y = kx\), where \(k\) is a constant. This means that the relationship passes through the origin (0,0) and does not have a constant added or subtracted.

Let's analyze each equation:

1. **y = x + 3**: This is not proportional because of the +3; it does not pass through the origin.

2. **y = 3x + 1**: This is not proportional because of the +1; it does not pass through the origin.

3. **y = 13x**: This is proportional because it fits the form \(y = kx\) (with \(k = 13\)), and it passes through the origin.

4. **y = \frac{1}{3}x**: This is also proportional because it fits the form \(y = kx\) (with \(k = \frac{1}{3}\)), and it passes through the origin.

5. **y = x^3 - 3**: This is not proportional due to the -3 and the cubic term; it does not pass through the origin and is not in the required linear form.

Thus, the equations that represent a proportional relationship are:

- **y = 13x**
- **y = \frac{1}{3}x**