Question: What is the slope of this line?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Graph: a line on a coordinate plane passing through the labeled points $(-2, 5)$ and $(2, -5)$, positioned center.
1. **State the problem:** Find the slope of the line passing through the points $(-2, 5)$ and $(2, -5)$.
2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:
$$m = \frac{y_2 - y_1}{x_2 - x_1}$$
3. **Substitute the given points:**
$$m = \frac{-5 - 5}{2 - (-2)}$$
4. **Simplify numerator and denominator:**
$$m = \frac{-10}{2 + 2}$$
$$m = \frac{-10}{4}$$
5. **Simplify the fraction by dividing numerator and denominator by 2:**
$$m = \frac{\cancel{-10}^{\div 2}}{\cancel{4}^{\div 2}} = \frac{-5}{2}$$
6. **Final answer:** The slope of the line is $\boxed{-\frac{5}{2}}$.
This means the line falls 5 units vertically for every 2 units it moves horizontally to the right.