To determine the slope of the line given by the equation [tex]\( y = \frac{1}{2} x + 4 \)[/tex], we need to identify the form of the equation used here. The equation of a line in slope-intercept form is given by:
[tex]\[ y = mx + b \][/tex]
Where:
- [tex]\( m \)[/tex] represents the slope of the line.
- [tex]\( b \)[/tex] represents the y-intercept, which is the point where the line crosses the y-axis.
In the given equation:
[tex]\[ y = \frac{1}{2} x + 4 \][/tex]
The coefficient of [tex]\( x \)[/tex] is [tex]\( \frac{1}{2} \)[/tex]. This coefficient directly represents the slope [tex]\( m \)[/tex] of the line.
Therefore, the slope [tex]\( m \)[/tex] of the line is:
[tex]\[ \frac{1}{2} \][/tex]
Hence, the correct answer is:
B. [tex]\( \frac{1}{2} \)[/tex]
