The problem provides the coordinates of four points: $P(1, 1)$, $Q(9, 8)$, $U(-6, 1)$, and $V(2, 8)$. We are not given a specific question, so it is unclear what needs to be calculated or determined. However, a likely question is to find the slopes of the lines $PQ$ and $UV$, and then compare them.

1. Problem Description

The problem provides the coordinates of four points: $P(1, 1)$, $Q(9, 8)$, $U(-6, 1)$, and $V(2, 8)$. We are not given a specific question, so it is unclear what needs to be calculated or determined. However, a likely question is to find the slopes of the lines $PQ$ and $UV$, and then compare them.

2. Solution Steps

First, we will calculate the slope of line $PQ$. The slope of a line between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

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

For points $P(1, 1)$ and $Q(9, 8)$, we have:

$m_{PQ} = \frac{8 - 1}{9 - 1} = \frac{7}{8}$

Next, we will calculate the slope of line $UV$. For points $U(-6, 1)$ and $V(2, 8)$, we have:

$m_{UV} = \frac{8 - 1}{2 - (-6)} = \frac{7}{2 + 6} = \frac{7}{8}$

Since $m_{PQ} = m_{UV}$, the lines $PQ$ and $UV$ are parallel.

3. Final Answer

The slope of line $PQ$ is $\frac{7}{8}$. The slope of line $UV$ is $\frac{7}{8}$. The lines $PQ$ and $UV$ are parallel because they have the same slope.