Final answer:
The slope of the equation Y = -1/2 X + 1/4 is -1/2, which is the coefficient of X in the slope-intercept form of a linear equation.
Step-by-step explanation:
The slope of the line represented by the equation Y = -1/2 X + 1/4 is -1/2. This equation is in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. In this form, the slope can be directly read as the coefficient of X, which in the given equation is -1/2.
This means for every one unit increase in X, Y decreases by 1/2 unit. A negative slope indicates that the line moves down the y-axis as the x-value increases, and the more negative the slope, the steeper the line descends.