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The problem involves finding the equation of a line that is parallel to the given line \( y = \frac{1}{2}x - 5 \) and passes through the point \( (0, 4) \).

### Step-by-step Solution:
1. **Parallel Lines**:
   - Parallel lines have the same slope. The slope of the given line \( y = \frac{1}{2}x - 5 \) is \( \frac{1}{2} \).
   - So, the new line that is parallel to this will also have the slope \( \frac{1}{2} \).

2. **Point-Slope Form**:
   - We know the slope is \( \frac{1}{2} \), and the new line passes through the point \( (0, 4) \).
   - Using the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we substitute \( x = 0 \) and \( y = 4 \) to find the new \( b \).

3. **Find the y-intercept**:
   - Substituting into the equation:
     \[
     y = \frac{1}{2}x + b
     \]
     \[
     4 = \frac{1}{2}(0) + b
     \]
     \[
     b = 4
     \]
   - So, the equation of the line is:
     \[
     y = \frac{1}{2}x + 4
     \]

4. **Conclusion**:
   - The equation that represents Lynda’s second cut is \( y = \frac{1}{2}x + 4 \), which matches option **B**.

Thus, the correct answer is **B**.

Would you like further details or clarifications?

### Related Questions:
1. How do we calculate the slope of a line given two points?
2. How can you verify if two lines are parallel?
3. What are the characteristics of perpendicular lines?
4. How do you find the equation of a line if you are given a slope and a point?
5. What is the difference between slope-intercept form and point-slope form?

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

Lynda cuts a piece of wood for a project. The first cut is shown and can be represented by the equation y = 1/2x - 5. The second cut needs to be parallel to the first. It will pass through the point (0, 4). Identify the equation that represents Lynda's second cut.

Solve the problem of finding the equation of a line that is parallel to y = 1/2x - 5 and passes through the point (0, 4). This problem covers algebra concepts, focusing on parallel lines and slope-intercept form, suitable for students in Grades 7-10.

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