Question: Answer
Attempt 1 out of 2
Slope of the Line:
The graph shows a blue line rising from left to right, crossing the y-axis at about -8 and passing near points $(-6, -9)$ and $(6, -7)$; position_hint = center
1. **State the problem:** Find the slope of the line passing through points $(-6, -9)$ and $(6, -7)$.
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 points:** Here, $x_1 = -6$, $y_1 = -9$, $x_2 = 6$, $y_2 = -7$.
$$m = \frac{-7 - (-9)}{6 - (-6)} = \frac{-7 + 9}{6 + 6}$$
4. **Simplify numerator and denominator:**
$$m = \frac{2}{12}$$
5. **Simplify the fraction by dividing numerator and denominator by 2:**
$$m = \frac{\cancel{2}^1}{\cancel{12}^6} = \frac{1}{6}$$
6. **Interpretation:** The slope $m = \frac{1}{6}$ means the line rises 1 unit vertically for every 6 units it moves horizontally to the right.
**Final answer:** The slope of the line is $\boxed{\frac{1}{6}}$.