Question

Classify the following as either proportional or not proportional.
Proportional
Not Proportional
y
=
2
3
x
y=
3
2
​
x








y
=
3
x
−
4
y=3x−4

Answer 1

To determine whether the relationships are proportional, we need to check if they can be expressed in the form \(y = kx\), where \(k\) is a constant. If a relationship can be written in this form, it is considered proportional. If it includes additional terms or constants (such as a constant added or subtracted from the product), it is not proportional.

1. **\(y = \frac{2}{3}x\)**: This is proportional since it can be written in the form \(y = kx\) where \(k = \frac{2}{3}\).
- **Classification**: Proportional

2. **\(y = \frac{3}{2}x\)**: This is also proportional since it follows the form \(y = kx\) where \(k = \frac{3}{2}\).
- **Classification**: Proportional

3. **\(y = 3x - 4\)**: This is not proportional because it includes the constant term \(-4\) in addition to the term \(3x\). This cannot be expressed in the form \(y = kx\).
- **Classification**: Not Proportional

In summary:
- \(y = \frac{2}{3}x\) → Proportional
- \(y = \frac{3}{2}x\) → Proportional
- \(y = 3x - 4\) → Not Proportional