We are asked to find the slope of a line that is parallel to the line passing through the points $(6,8)$ and $(24,4)$.

1. Problem Description

We are asked to find the slope of a line that is parallel to the line passing through the points $(6,8)$ and $(24,4)$.

2. Solution Steps

First, we need to find the slope of the line passing through the points $(6,8)$ and $(24,4)$. The formula for the slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

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

Plugging in the given points $(6,8)$ and $(24,4)$, we have:

$$m = \frac{4 - 8}{24 - 6} = \frac{-4}{18} = -\frac{2}{9}$$

Since parallel lines have the same slope, the slope of the line parallel to the line passing through the points $(6,8)$ and $(24,4)$ is also $-\frac{2}{9}$.

3. Final Answer

The slope of the parallel line is $-\frac{2}{9}$.