1. **State the problem:** We are given a relation M with points $(x, y)$ as follows: $(-1, 3)$, $(0, 6)$, $(2, 12)$, and $(3, 15)$. We need to determine the nature of the rate of change between $x$ and $y$ values. 2. **Recall the formula for rate of change:** The rate of change between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the slope formula: $$\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}$$ A constant rate of change means the slope is the same between every pair of consecutive points. 3. **Calculate the rate of change between consecutive points:** - Between $(-1, 3)$ and $(0, 6)$: $$\frac{6 - 3}{0 - (-1)} = \frac{3}{1} = 3$$ - Between $(0, 6)$ and $(2, 12)$: $$\frac{12 - 6}{2 - 0} = \frac{6}{2} = 3$$ - Between $(2, 12)$ and $(3, 15)$: $$\frac{15 - 12}{3 - 2} = \frac{3}{1} = 3$$ 4. **Interpretation:** Since the rate of change (slope) is $3$ between every pair of consecutive points, the relation has a constant rate of change. 5. **Conclusion:** The relation M could represent a linear relationship because it has a constant rate of change between the $x$- and $y$-values. **Final answer:** The relation has a constant rate of change between the $x$- and $y$-values and could represent a linear relationship.