To determine the slope of a line parallel to the given line [tex]\( y = \frac{1}{2} x + 6 \)[/tex], let's follow these steps:
1. Identify the Slope of the Given Line:
- The equation [tex]\( y = \frac{1}{2} x + 6 \)[/tex] is in the slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
- Here, the slope [tex]\( m \)[/tex] is [tex]\( \frac{1}{2} \)[/tex].
2. Understand Parallel Line Slopes:
- Parallel lines have the same slope. This means that if a line is parallel to the given line, it will also have a slope of [tex]\( \frac{1}{2} \)[/tex].
3. Conclusion:
- Therefore, the slope of a line parallel to the given line [tex]\( y = \frac{1}{2} x + 6 \)[/tex] is [tex]\( \frac{1}{2} \)[/tex].
So, the correct answer is:
A) [tex]\( \frac{1}{2} \)[/tex]
