Question: Find the slope of the line.
Slope = m =
Enter your answer as an integer or as a reduced fraction in the form A/B.
Graph: a red line rises from bottom-left to top-right, crossing the y-axis at (0, -2) and passing through (2, 1); position_hint = center
1. **State the problem:** We need to find the slope $m$ of the line passing through the points $(0, -2)$ and $(2, 1)$.
2. **Formula for slope:** The slope $m$ of a line passing 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. **Identify points:** Here, $x_1 = 0$, $y_1 = -2$, $x_2 = 2$, and $y_2 = 1$.
4. **Substitute values:**
$$m = \frac{1 - (-2)}{2 - 0} = \frac{1 + 2}{2} = \frac{3}{2}$$
5. **Simplify:** The fraction $\frac{3}{2}$ is already in reduced form.
6. **Interpretation:** The slope $m = \frac{3}{2}$ means the line rises 3 units vertically for every 2 units it moves horizontally to the right.
**Final answer:**
$$m = \frac{3}{2}$$