The problem asks to calculate the slopes of two lines. The first line passes through the points $P(-10, 7)$ and $Q(2, 1)$. The second line passes through the points $U(4, 0)$ and $V(6, 1)$.

1. Problem Description

The problem asks to calculate the slopes of two lines. The first line passes through the points $P(-10, 7)$ and $Q(2, 1)$. The second line passes through the points $U(4, 0)$ and $V(6, 1)$.

2. Solution Steps

To find the slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$, we use the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

For the line passing through $P(-10, 7)$ and $Q(2, 1)$, we have $x_1 = -10$, $y_1 = 7$, $x_2 = 2$, and $y_2 = 1$. Plugging these values into the slope formula, we get:

$m_{PQ} = \frac{1 - 7}{2 - (-10)} = \frac{-6}{2 + 10} = \frac{-6}{12} = -\frac{1}{2}$

For the line passing through $U(4, 0)$ and $V(6, 1)$, we have $x_1 = 4$, $y_1 = 0$, $x_2 = 6$, and $y_2 = 1$. Plugging these values into the slope formula, we get:

$m_{UV} = \frac{1 - 0}{6 - 4} = \frac{1}{2}$

3. Final Answer

The slope of the line passing through points $P$ and $Q$ is $-\frac{1}{2}$.

The slope of the line passing through points $U$ and $V$ is $\frac{1}{2}$.