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The problem asks to write the equation of a line in slope-intercept form that passes through the point (-8, 6) and is parallel to the line given by the equation:

\[
y = -\frac{1}{4}x + 5
\]

### Step-by-step solution:

1. **Identify the slope**:  
   The equation of the given line is in slope-intercept form \( y = mx + b \), where \( m \) is the slope.  
   From \( y = -\frac{1}{4}x + 5 \), we can see that the slope \( m = -\frac{1}{4} \).

2. **Parallel lines**:  
   Parallel lines have the same slope. Therefore, the line we are looking for will also have a slope of \( m = -\frac{1}{4} \).

3. **Point-slope form**:  
   To find the equation of the line, use the point-slope form of a line equation:
   \[
   y - y_1 = m(x - x_1)
   \]
   where \( (x_1, y_1) \) is the point the line passes through and \( m \) is the slope.  
   Here, the point is \( (-8, 6) \) and the slope is \( -\frac{1}{4} \).

   Substituting these values into the point-slope form:
   \[
   y - 6 = -\frac{1}{4}(x - (-8))
   \]
   Simplify the expression:
   \[
   y - 6 = -\frac{1}{4}(x + 8)
   \]
   Distribute the slope:
   \[
   y - 6 = -\frac{1}{4}x - 2
   \]

4. **Solve for \( y \)**:  
   Now, add 6 to both sides to put the equation in slope-intercept form:
   \[
   y = -\frac{1}{4}x - 2 + 6
   \]
   Simplifying the constant term:
   \[
   y = -\frac{1}{4}x + 4
   \]

### Final Answer:
The equation of the line in slope-intercept form is:
\[
y = -\frac{1}{4}x + 4
\]

Would you like further details or have any questions?

Here are some related questions to consider:
1. What is the significance of the slope in the slope-intercept form of a line?
2. How do you determine the slope of a line from its equation?
3. What happens to the equation of a line if it is perpendicular rather than parallel?
4. How would the equation change if the point given was different, such as (2, 3)?
5. What steps would you take if the equation of the original line was not in slope-intercept form?

**Tip:** When writing equations of lines, always ensure you know whether you're dealing with parallel or perpendicular lines as this affects the slope.

Write an equation of the line in slope-intercept form that passes through the given point (-8, 6) and is parallel to the graph of the equation y = -(1/4)x + 5.

This problem involves writing the equation of a line in slope-intercept form that passes through (-8, 6) and is parallel to y = -(1/4)x + 5. It covers key algebraic concepts like parallel lines, slope-intercept form, and point-slope form.

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