To determine the slope of line [tex]\( b \)[/tex], we need to use the information given and the properties of parallel lines.
1. Understanding the Concept: Parallel lines have the characteristic that their slopes are equal. This is a fundamental property in geometry and coordinate algebra. Therefore, if two lines are parallel, their slopes must be identical.
2. Given Information: We are provided that the slope of line [tex]\( a \)[/tex] is [tex]\(\frac{1}{4}\)[/tex].
3. Applying Properties of Parallel Lines: Since lines [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are parallel, the slope of line [tex]\( b \)[/tex] must be the same as the slope of line [tex]\( a \)[/tex].
4. Conclusion: Therefore, the slope of line [tex]\( b \)[/tex] is also [tex]\(\frac{1}{4}\)[/tex].
So, the correct answer is:
[tex]\[ \boxed{\frac{1}{4}} \][/tex]
