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.
Click twice to plot each segment.
Click a segment to delete it.
Graph: A downward-sloping line passes through the points $(-3, 0)$ and $(0, -2)$, extending from the top-left to the bottom-right; the shown rise/run markers indicate a rise of $-2$ and a run of $3$, so the slope is $-\frac{2}{3}$. position_hint = center
1. **State the problem:**
We are given two points on a line: $(-3, 0)$ and $(0, -2)$. We need to find the slope of the line by representing the rise and run.
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. **Calculate the rise and run:**
- Rise (change in $y$): $y_2 - y_1 = -2 - 0 = -2$
- Run (change in $x$): $x_2 - x_1 = 0 - (-3) = 3$
4. **Calculate the slope:**
$$m = \frac{-2}{3}$$
5. **Simplify the slope:**
The fraction $-\frac{2}{3}$ is already in simplest form.
6. **Interpretation:**
The slope is negative, indicating the line slopes downward from left to right.
**Final answer:**
The slope of the line is $-\frac{2}{3}$.