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The problem asks for the equation of a line that is perpendicular to the line \( y = 2x + 1 \) and passes through the point \( (-8, 4) \).

### Step-by-step solution:

1. **Identify the slope of the given line**:  
   The equation of the given line is \( y = 2x + 1 \). Here, the slope (m) is 2.

2. **Find the slope of the perpendicular line**:  
   The slopes of two perpendicular lines are negative reciprocals of each other. So, the slope of the perpendicular line will be \( m = -\frac{1}{2} \).

3. **Use the point-slope form of the equation of a line**:  
   The point-slope form is \( y - y_1 = m(x - x_1) \), where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope.  
   Substituting \( m = -\frac{1}{2} \), \( x_1 = -8 \), and \( y_1 = 4 \):
   \[
   y - 4 = -\frac{1}{2}(x + 8)
   \]

4. **Simplify the equation**:
   Distribute the slope:
   \[
   y - 4 = -\frac{1}{2}x - 4
   \]
   Add 4 to both sides:
   \[
   y = -\frac{1}{2}x
   \]

So, the equation of the line is \( y = -\frac{1}{2}x \).

### Answer:
The correct option is **B: \( y = -\frac{1}{2}x \)**.

Would you like more details on any of the steps, or have any questions?

Here are 5 related questions to practice:
1. How do you find the slope of a line from its equation in standard form?
2. What is the equation of a line parallel to \( y = 3x + 5 \) passing through \( (2, -1) \)?
3. How do you derive the equation of a line given two points?
4. Can two lines with the same slope be perpendicular?
5. What is the point-slope form of the equation of a line?

**Tip:** For perpendicular lines, always remember to take the negative reciprocal of the slope!

Write the equation of the line that is perpendicular to y = 2x + 1 and passes through (-8, 4).

Learn how to find the equation of a line that is perpendicular to y = 2x + 1 and passes through (-8, 4). This step-by-step solution covers point-slope form and perpendicular line slopes, suitable for students in Grades 8-10.

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