Question: What is the slope of the line that goes through points $A$ and $B$?
What is another way to write the slope of the line?
Point $A : (-1, 6)$ Point $B : (5, 4)$
Slope = vertical distance
-------------------
horizontal distance
= $6 - 4$
------
$-1 - 5$
= $2$
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$-6$
= [ ]
$\frac{1}{3}$ $3$ $-\frac{1}{2}$ $-\frac{1}{3}$ $\frac{1}{2}$
1. **State the problem:** Find the slope of the line passing through points $A(-1,6)$ and $B(5,4)$.
2. **Recall the slope formula:**
$$m = \frac{\text{vertical change}}{\text{horizontal change}} = \frac{y_2 - y_1}{x_2 - x_1}$$
where $(x_1,y_1)$ and $(x_2,y_2)$ are coordinates of points $A$ and $B$ respectively.
3. **Substitute the given points:**
$$m = \frac{4 - 6}{5 - (-1)} = \frac{4 - 6}{5 + 1}$$
4. **Calculate numerator and denominator:**
$$m = \frac{-2}{6}$$
5. **Simplify the fraction:**
$$m = \frac{\cancel{-2}}{\cancel{6}} = -\frac{1}{3}$$
6. **Interpretation:** The slope is $-\frac{1}{3}$, which means for every 3 units moved horizontally to the right, the line goes down by 1 unit.
7. **Another way to write the slope:**
The slope can also be expressed as the ratio of vertical distance to horizontal distance:
$$\text{slope} = \frac{\text{vertical distance}}{\text{horizontal distance}} = -\frac{1}{3}$$
**Final answer:**
$$\boxed{-\frac{1}{3}}$$