1. **Stating the problem:** We are given the mass $y$ (in grams) of an ice cube with side length $x$ (in cm) as follows: | $x$ | 1 | 2 | 3 | 4 | 5 | |-----|---|---|---|---|---| | $y$ | 0.9 | 7.2 | 24.3 | 57.6 | 112.5 | We want to form an equation relating $y$ to $x^3$. 2. **Understanding the relationship:** Since the mass of a cube is proportional to its volume, and volume $V = x^3$, we expect $y$ to be proportional to $x^3$. This means: $$y = k x^3$$ where $k$ is the constant of proportionality. 3. **Find the constant $k$ using the data:** Using the first data point where $x=1$ and $y=0.9$: $$0.9 = k \times 1^3 = k$$ So, $$k = 0.9$$ 4. **Form the equation:** $$\boxed{y = 0.9 x^3}$$ 5. **Describe the change in $y$ when $x$ is halved:** If $x$ is halved, then $x$ becomes $\frac{x}{2}$. Substitute into the equation: $$y_{new} = 0.9 \left(\frac{x}{2}\right)^3 = 0.9 \frac{x^3}{8} = \frac{y}{8}$$ This means the mass $y$ becomes one-eighth of its original value when the side length $x$ is halved. **Summary:** - The equation relating mass $y$ to side length $x$ is $y = 0.9 x^3$. - When $x$ is halved, $y$ reduces to one-eighth of its original value.