To find the slope of the line represented by the equation [tex]\( y = -\frac{1}{2} x + \frac{1}{4} \)[/tex], let's break down the equation and understand its form.
The equation given is in the slope-intercept form of a linear equation, which is generally written as:
[tex]\[ y = mx + b \][/tex]
Here:
- [tex]\( m \)[/tex] represents the slope of the line.
- [tex]\( b \)[/tex] represents the y-intercept of the line, which is the point where the line crosses the y-axis.
In the provided equation:
[tex]\[ y = -\frac{1}{2} x + \frac{1}{4} \][/tex]
we can identify the coefficient of [tex]\( x \)[/tex] to determine the slope. The coefficient of [tex]\( x \)[/tex] is [tex]\( -\frac{1}{2} \)[/tex].
Thus, the slope [tex]\( m \)[/tex] of the line is:
[tex]\[ m = -\frac{1}{2} \][/tex]
So, the correct answer is:
[tex]\[ -\frac{1}{2} \][/tex]
Therefore, 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 choice is:
[tex]\[ -\frac{1}{2} \][/tex]
