To find the equation of the line that passes through the point $(4, 4)$ and is parallel to the line $y = \frac{1}{2}x + 4$, follow these steps:

1. Identify the Slope of the Given Line: Since the line is parallel, it will have the same slope as the line $y = \frac{1}{2}x + 4$. The slope of this line is $\frac{1}{2}$.

2. Use the Point-Slope Form of the Line: The point-slope form of a line equation is: $y - y_1 = m(x - x_1)$ where $m$ is the slope and $(x_1, y_1)$ is a point on the line. Here, $m = \frac{1}{2}$ and $(x_1, y_1) = (4, 4)$.

3. Substitute and Simplify: Plugging in the values, we get: $y - 4 = \frac{1}{2}(x - 4)$

   Expanding this: $y - 4 = \frac{1}{2}x - 2$

   Then, isolate $y$: $y = \frac{1}{2}x + 2$

4. Identify $B$ (the y-intercept): The equation of the line we found is $y = \frac{1}{2}x + 2$. Here, $B = 2$, which is the y-intercept of this line.

Answer:

The y-intercept, $B$, is $2$.

Would you like additional details on this process or have any other questions?

Here are related questions for further practice:

1. How would you find the equation of a line perpendicular to $y = \frac{1}{2}x + 4$ passing through $(4,4)$?
2. If a line passes through $(4,4)$ and has a slope of $-\frac{1}{2}$, what is its equation?
3. What is the general formula to find the slope-intercept form of a line given a point and a slope?
4. How do you find the point where two lines intersect if you know their equations?
5. How does the slope of parallel lines compare to the slope of perpendicular lines?

Tip: Remember, parallel lines always have identical slopes, while perpendicular lines have slopes that are negative reciprocals of each other.