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.