To determine the slope of the line represented by the equation [tex]\( y = -\frac{1}{2} x + \frac{1}{4} \)[/tex], follow these steps:
1. Identify the form of the line's equation:
- The given equation is in the slope-intercept form, which is [tex]\( y = mx + b \)[/tex].
- In this form, [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the y-intercept.
2. Extract the slope:
- Compare the given equation [tex]\( y = -\frac{1}{2} x + \frac{1}{4} \)[/tex] with the general slope-intercept form [tex]\( y = mx + b \)[/tex].
- Here, [tex]\( m = -\frac{1}{2} \)[/tex].
Therefore, the slope of the line is [tex]\( -\frac{1}{2} \)[/tex].
Among the provided options:
- [tex]\( -\frac{1}{2} \)[/tex] (Correct answer)
- [tex]\( -\frac{1}{4} \)[/tex]
- [tex]\( \frac{1}{4} \)[/tex]
- [tex]\( \frac{1}{2} \)[/tex]
The correct answer is [tex]\( -\frac{1}{2} \)[/tex].
