Question: Draw a line representing the “rise” and a line representing the “run” of the line.
State the slope of the line in simplest form.
Click twice to plot each segment.
Click a segment to delete it.
y
x
The graph shows a straight line decreasing from left to right, passing through the points $(-3, 0)$ and $(1, -3)$. The rise/run is down 3 and right 4, so the slope is $-3/4$.
1. **State the problem:** We need to find the slope of the line passing through the points $(-3, 0)$ and $(1, -3)$ and represent the "rise" and "run" visually.
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. **Calculate the rise and run:**
- Rise $= y_2 - y_1 = -3 - 0 = -3$
- Run $= x_2 - x_1 = 1 - (-3) = 1 + 3 = 4$
4. **Calculate the slope:**
$$m = \frac{-3}{4}$$
5. **Interpretation:** The slope is negative, indicating the line decreases as $x$ increases.
6. **Simplify:** The fraction $\frac{-3}{4}$ is already in simplest form.
7. **Visual representation:** The "rise" is a vertical line segment down 3 units, and the "run" is a horizontal line segment right 4 units between the points.
**Final answer:** The slope of the line is $-\frac{3}{4}$.