We are given the coordinates of the vertices of quadrilateral $WXYZ$: $W(6, 8)$, $X(3, -3)$, $Y(-3, -3)$, and $Z(-6, 8)$. We need to find the slopes of the line segments $ZY$ and $WX$.

1. Problem Description

We are given the coordinates of the vertices of quadrilateral $WXYZ$: $W(6, 8)$, $X(3, -3)$, $Y(-3, -3)$, and $Z(-6, 8)$. We need to find the slopes of the line segments $ZY$ and $WX$.

2. Solution Steps

The slope of a line segment between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:

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

First, let's find the slope of $ZY$. The coordinates of $Z$ are $(-6, 8)$ and the coordinates of $Y$ are $(-3, -3)$. Let $Z = (x_1, y_1) = (-6, 8)$ and $Y = (x_2, y_2) = (-3, -3)$.

$m_{ZY} = \frac{-3 - 8}{-3 - (-6)} = \frac{-11}{-3 + 6} = \frac{-11}{3}$

Next, let's find the slope of $WX$. The coordinates of $W$ are $(6, 8)$ and the coordinates of $X$ are $(3, -3)$. Let $W = (x_1, y_1) = (6, 8)$ and $X = (x_2, y_2) = (3, -3)$.

$m_{WX} = \frac{-3 - 8}{3 - 6} = \frac{-11}{-3} = \frac{11}{3}$

3. Final Answer

Slope of $ZY$: $-\frac{11}{3}$

Slope of $WX$: $\frac{11}{3}$