To find the slope of a line parallel to a given line, we first need to understand the concept of parallel lines in coordinate geometry. Two lines are parallel if and only if they have the same slope.
The equation given in the question is:
[tex]\[ y = \frac{1}{2} x + 6 \][/tex]
This equation is in the slope-intercept form, [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope of the line, and [tex]\( b \)[/tex] is the y-intercept.
In the given equation:
[tex]\[ y = \frac{1}{2} x + 6 \][/tex]
The slope [tex]\( m \)[/tex] is [tex]\( \frac{1}{2} \)[/tex].
So, for a line to be parallel to this given line, it must have the same slope. Therefore, the slope of a line parallel to the given line is:
[tex]\[ \frac{1}{2} \][/tex]
Thus, the correct answer is:
A) [tex]\( \frac{1}{2} \)[/tex]
