Classify the following as either proportional or not proportional.

Question

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