Here is the graph showing the perpendicular line $y = -2x$ in blue and the original line $y = \frac{1}{2}x + 3$ in green. The red point represents the coordinates $(4, -8)$, through which the perpendicular line passes.

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. How do you find the slope of a line given two points?
2. What is the slope of a line parallel to $y = 3x + 7$?
3. How would the equation change if the line passed through $(0, 0)$?
4. What is the general formula for finding perpendicular lines in 3D space?
5. How can you determine if two lines are parallel without graphing?

Tip: When solving for perpendicular slopes, remember that the product of the slopes of two perpendicular lines always equals $-1$.