The equation of the line given is in slope-intercept form:

$y = \frac{1}{2}x + 2$

From this, we can identify that the slope $m$ of the line is $\frac{1}{2}$.

For any line parallel to this one, the slope will remain the same. Therefore, the slope of the new line that we need to find will also be $\frac{1}{2}$.

Now, we have the slope of the new line, and we are also given the point through which the new line passes: $(4, 5)$.

Step 1: Use the point-slope form of the line equation

The point-slope form of the equation 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. Substituting $m = \frac{1}{2}$, $x_1 = 4$, and $y_1 = 5$:

$y - 5 = \frac{1}{2}(x - 4)$

Step 2: Simplify the equation to slope-intercept form

Now, simplify the equation:

$y - 5 = \frac{1}{2}(x - 4)$ $y - 5 = \frac{1}{2}x - 2$ $y = \frac{1}{2}x - 2 + 5$ $y = \frac{1}{2}x + 3$

Thus, the equation of the line parallel to $y = \frac{1}{2}x + 2$ that passes through the point $(4, 5)$ is:

$y = \frac{1}{2}x + 3$

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Would you like further details on this, or do you have any other questions?

Related questions:

1. How can I find the slope of a line given two points on it?
2. What is the general form of the equation of a line?
3. How can I graph a line using its equation?
4. What is the point-slope form of a linear equation, and how is it derived?
5. How does the slope of parallel lines compare to that of perpendicular lines?

Tip: When writing the equation of a line in slope-intercept form, remember to identify the slope and the y-intercept clearly to avoid mistakes!