What is the slope of the line represented by the equation \( y=-\frac{1}{2} x+\frac{1}{4} \) ? \( -\frac{1}{2} \) \( -\frac{1}{4} \) \( \frac{1}{2} \)

The slope of the line in the equation \( y=-\frac{1}{2} x+\frac{1}{4} \) is the coefficient of \( x \), which is \( -\frac{1}{2} \). This means that for every increase of 1 in \( x \), \( y \) decreases by \( \frac{1}{2} \). So, the line slopes downwards from left to right, creating a negative relationship between \( x \) and \( y \). In real-world terms, if you think of the line as representing the relationship between time spent studying (x-axis) and exam performance (y-axis), a slope of \( -\frac{1}{2} \) would suggest that increasing study time can slightly lower performance, which seems counterintuitive! It highlights the importance of balanced study routines rather than excessive cramming.