Question: Draw a line representing the $\text{rise}$ and a line representing the $\text{run}$ of the line. State the slope of the line in simplest form.
1. **State the problem:** We need to find the slope of the line passing through the points approximately $(0,1)$ and $(4,4)$.
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:** From the graph, the points are $A(0,1)$ and $B(4,4)$.
4. **Calculate rise and run:**
- Rise $= y_2 - y_1 = 4 - 1 = 3$
- Run $= x_2 - x_1 = 4 - 0 = 4$
5. **Calculate slope:**
$$m = \frac{3}{4}$$
6. **Simplify slope:** The fraction $\frac{3}{4}$ is already in simplest form.
7. **Interpretation:** The slope $\frac{3}{4}$ means for every 4 units moved horizontally (run), the line rises 3 units vertically (rise).