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To solve the problem, we need to find the equation of a line that is **parallel** to the given line \( y = -\frac{1}{2}x - 7 \) and passes through the point \( A(-6, 5) \).

### Step-by-step Solution:

1. **Identify the slope of the given line**: 
   The equation of the given line is \( y = -\frac{1}{2}x - 7 \). In slope-intercept form \( y = mx + b \), the coefficient \( m \) represents the slope. Thus, the slope of the given line is \( m = -\frac{1}{2} \).

2. **Use the fact that parallel lines have the same slope**: 
   Since the new line must be parallel to the given line, it will also have the same slope \( m = -\frac{1}{2} \).

3. **Use the point-slope form of the equation of a line**:
   The point-slope form is given by:
   \[
   y - y_1 = m(x - x_1)
   \]
   where \( (x_1, y_1) \) is the point through which the line passes, and \( m \) is the slope.
   - Substituting \( m = -\frac{1}{2} \), \( x_1 = -6 \), and \( y_1 = 5 \), we get:
   \[
   y - 5 = -\frac{1}{2}(x - (-6))
   \]
   Simplifying this:
   \[
   y - 5 = -\frac{1}{2}(x + 6)
   \]
   Distribute the slope \( -\frac{1}{2} \):
   \[
   y - 5 = -\frac{1}{2}x - 3
   \]
   Add 5 to both sides to solve for \( y \):
   \[
   y = -\frac{1}{2}x - 3 + 5
   \]
   \[
   y = -\frac{1}{2}x + 2
   \]

Thus, the equation of the line that is parallel to \( y = -\frac{1}{2}x - 7 \) and passes through the point \( A(-6, 5) \) is:
\[
y = -\frac{1}{2}x + 2
\]

Let me know if you would like more details or have any further questions! Here are some related questions:

1. How do you find the equation of a line perpendicular to a given line?
2. What is the difference between slope-intercept form and point-slope form?
3. How would the equation change if the line passed through a different point?
4. How can we find the x- and y-intercepts of the line \( y = -\frac{1}{2}x + 2 \)?
5. What happens to the slope if two lines are perpendicular to each other?

**Tip**: Parallel lines always have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other.

Write an equation of the line passing through the point A(-6, 5) that is parallel to the line y = -1/2x - 7.

Learn how to write the equation of a line passing through point A(-6, 5) that is parallel to y = -1/2x - 7. This problem covers key algebraic concepts, including slope-intercept form, point-slope form, and properties of parallel lines. Suitable for students in Grades 8-10.

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