Line through the points `(-2, 6)`and `(4, 8)`is perpendicular to the line through the points `(8, 12)`and `(x , 24)`. Find the value of x.

Explanation

To find the value of \( x \) such that the line through the points \((-2, 6)\) and \( (4, 8) \) is perpendicular to the line through the points \( (8, 12) \) and \( (x, 24) \), we will follow these steps:

### Step 1: Calculate the slope of the line through points \((-2, 6)\) and \( (4, 8) \).

The formula for the slope \( m \) 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}
...