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