To determine the slope of the line represented by the equation [tex]\( y = \frac{1}{2} x + \frac{1}{4} \)[/tex], we start by recalling the general form of a linear equation in slope-intercept form, which is given by:
[tex]\[ y = mx + c \][/tex]
In this form:
- [tex]\( m \)[/tex] represents the slope of the line.
- [tex]\( c \)[/tex] represents the y-intercept of the line.
Now, comparing our given equation [tex]\( y = \frac{1}{2} x + \frac{1}{4} \)[/tex] with the slope-intercept form:
- The coefficient of [tex]\( x \)[/tex] (which is [tex]\(\frac{1}{2}\)[/tex]) corresponds to [tex]\( m \)[/tex].
- The constant term (which is [tex]\(\frac{1}{4}\)[/tex]) corresponds to [tex]\( c \)[/tex].
From this, we can see that the slope of the line is:
[tex]\[ m = \frac{1}{2} \][/tex]
Thus, the slope of the line represented by the equation [tex]\( y = \frac{1}{2} x + \frac{1}{4} \)[/tex] is:
[tex]\[ \frac{1}{2} \][/tex]
So, the correct answer is:
[tex]\(\boxed{\frac{1}{2}}\)[/tex]
