The problem asks whether the equation $y = 7x^3$ is proportional or not.

1. Problem Description

The problem asks whether the equation $y = 7x^3$ is proportional or not.

2. Solution Steps

A proportional relationship is a relationship between two variables in which their ratio is constant. This can be expressed in the form $y = kx$, where $k$ is the constant of proportionality.

The given equation is $y = 7x^3$. This equation can be written as $y = 7 \cdot x \cdot x \cdot x$.

If we want to express this in the form $y = kx$, we would need $k = 7x^2$, but $k$ must be constant for the relationship to be proportional.

Since $k$ is not a constant in this case, the equation is not proportional.

Also, when $x=0$, $y=7(0)^3=0$. This point is $(0, 0)$.

If $x=1$, $y=7(1)^3 = 7$. This point is $(1, 7)$.

If $x=2$, $y=7(2)^3 = 7(8) = 56$. This point is $(2, 56)$.

The ratio of $y/x$ when $x=1$ is $7/1 = 7$.

The ratio of $y/x$ when $x=2$ is $56/2 = 28$.

Since the ratios are not the same, the equation is not proportional.

3. Final Answer

Non-Proportional