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The question asks to find the equation of a line \( l \) that passes through the point \( (3, -2) \) and is parallel to the line given by the equation \( y = \frac{1}{2}x + 5 \).

### Step 1: Identify the slope of the given line
The equation of the given line is \( y = \frac{1}{2}x + 5 \). This is in slope-intercept form \( y = mx + b \), where \( m \) is the slope. So, the slope of the given line is \( \frac{1}{2} \).

### Step 2: Parallel lines have the same slope
Since the line \( l \) is parallel to this given line, the slope of \( l \) will also be \( \frac{1}{2} \).

### Step 3: Use the point-slope form of the equation
The point-slope form of a line is:
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope and \( (x_1, y_1) \) is the point on the line. For the line \( l \), we have:
- Slope \( m = \frac{1}{2} \)
- Point \( (x_1, y_1) = (3, -2) \)

Substituting these values into the point-slope form:
\[
y - (-2) = \frac{1}{2}(x - 3)
\]
\[
y + 2 = \frac{1}{2}(x - 3)
\]
Now simplify:
\[
y + 2 = \frac{1}{2}x - \frac{3}{2}
\]
\[
y = \frac{1}{2}x - \frac{3}{2} - 2
\]
\[
y = \frac{1}{2}x - \frac{7}{2}
\]

### Step 4: Convert to standard form
To convert this equation to standard form \( Ax + By + C = 0 \), first multiply through by 2 to eliminate the fraction:
\[
2y = x - 7
\]
Now, move all terms to one side:
\[
x - 2y - 7 = 0
\]

Thus, the equation of the line is \( x - 2y - 7 = 0 \), which corresponds to option **B**.

### Final Answer:
The correct option is **B**.

Would you like any additional clarification or details on the steps? 

Here are five related questions to consider:
1. How do you determine the equation of a line perpendicular to a given line?
2. What is the general form of a line's equation, and how do you convert between different forms?
3. How do you find the distance between two parallel lines?
4. How can you check if two lines are parallel using their equations?
5. What is the geometric significance of the slope of a line?

**Tip:** Parallel lines always share the same slope, which makes it easy to find their equations if a point on one line is known.

The line l passes through (3, -2) and is parallel to the line with the equation y = 1/2x + 5. What is the equation of l?

Solve for the equation of a line parallel to y = 1/2x + 5 and passing through the point (3, -2). Learn how to apply the point-slope formula and convert to standard form. Suitable for students in Grades 8-10.

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