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We are tasked with finding the equation of line \( k \), which is parallel to line \( j \). The equation for line \( j \) is given as:

\[
y = \frac{1}{2}x - 4
\]

### Step 1: Identify the slope of line \( j \)
The slope-intercept form of a line is:

\[
y = mx + b
\]

where \( m \) is the slope. From the equation \( y = \frac{1}{2}x - 4 \), we see that the slope \( m \) is \( \frac{1}{2} \).

### Step 2: Use the same slope for line \( k \)
Since line \( k \) is parallel to line \( j \), they share the same slope. Therefore, the slope of line \( k \) is also \( \frac{1}{2} \).

### Step 3: Use the point-slope form
We are given that line \( k \) passes through the point \( (-8, -5) \). To find the equation of line \( k \), we use the point-slope form of a line:

\[
y - y_1 = m(x - x_1)
\]

where \( m \) is the slope and \( (x_1, y_1) \) is the point the line passes through. Substituting the values:

- \( m = \frac{1}{2} \)
- \( x_1 = -8 \)
- \( y_1 = -5 \)

we get:

\[
y - (-5) = \frac{1}{2}(x - (-8))
\]

This simplifies to:

\[
y + 5 = \frac{1}{2}(x + 8)
\]

### Step 4: Solve for \( y \)
Now we solve for \( y \) to put the equation into slope-intercept form:

\[
y + 5 = \frac{1}{2}x + \frac{1}{2}(8)
\]
\[
y + 5 = \frac{1}{2}x + 4
\]
\[
y = \frac{1}{2}x + 4 - 5
\]
\[
y = \frac{1}{2}x - 1
\]

### Final Answer:
The equation of line \( k \) is:

\[
y = \frac{1}{2}x - 1
\]

Would you like more details on any of the steps?

Here are some additional questions related to this problem:

1. How do you find the slope of a line given two points on the line?
2. What is the difference between parallel and perpendicular lines in terms of their slopes?
3. How can you convert the equation of a line from point-slope form to slope-intercept form?
4. What would the equation of line \( k \) be if it were perpendicular to line \( j \) instead?
5. How do you check if a given point lies on a line?

**Tip**: When two lines are parallel, their slopes are always equal!

The equation for line j can be written as y = 1/2x - 4. Parallel to line j is line k, which passes through the point (-8, -5). What is the equation of line k?

Learn how to find the equation of a line parallel to y = 1/2x - 4, passing through the point (-8, -5). This tutorial explains key concepts such as slope-intercept and point-slope forms, along with step-by-step solutions.

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