Question: Find the slopes of lines $m$ and $n$.
Line $n$ goes through points $A$ and $B$. What is the slope of line $n$? Solve on paper, then enter your answer on Zearn.
Point $A : (5, 6)$
Point $B : (15, 12)$
The slope of line $n$ is
.
1. **State the problem:** Find the slope of line $n$ passing through points $A(5,6)$ and $B(15,12)$.
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. **Apply the formula:** Substitute $x_1=5$, $y_1=6$, $x_2=15$, and $y_2=12$:
$$m = \frac{12 - 6}{15 - 5}$$
4. **Calculate numerator and denominator:**
$$m = \frac{6}{10}$$
5. **Simplify the fraction:**
$$m = \frac{\cancel{6}}{\cancel{10}} = \frac{3}{5}$$
6. **Interpretation:** The slope of line $n$ is $\frac{3}{5}$, meaning for every 5 units moved horizontally, the line rises 3 units vertically.
**Final answer:**
$$\boxed{\frac{3}{5}}$$