1. **State the problem:** We are given data points with $x = -7, 0, 7, 14, 21$ and corresponding $y = -1, 2, 5, 8, 11$. We need to find the rate of change represented by this data.
2. **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:
$$\text{Rate of change} = \frac{y_2 - y_1}{x_2 - x_1}$$
This represents how much $y$ changes for a unit change in $x$.
3. **Calculate rate of change between consecutive points:**
- Between $(-7, -1)$ and $(0, 2)$:
$$\frac{2 - (-1)}{0 - (-7)} = \frac{3}{7}$$
- Between $(0, 2)$ and $(7, 5)$:
$$\frac{5 - 2}{7 - 0} = \frac{3}{7}$$
- Between $(7, 5)$ and $(14, 8)$:
$$\frac{8 - 5}{14 - 7} = \frac{3}{7}$$
- Between $(14, 8)$ and $(21, 11)$:
$$\frac{11 - 8}{21 - 14} = \frac{3}{7}$$
4. **Interpretation:** The rate of change is constant and equal to $\frac{3}{7}$ for all intervals, indicating a linear relationship.
5. **Final answer:** The rate of change represented by the data is $\boxed{\frac{3}{7}}$.
Rate Of Change
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