A line has a slope of \( -\frac{1}{2} \) and a \( y \)-intercept of \( -\frac{1}{2} \). Write its equation in slope-intercept form.

The equation of a line in slope-intercept form is given by \( y = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept. For the given line, the slope \( m \) is \( -\frac{1}{2} \) and the \( y \)-intercept \( b \) is \( -\frac{1}{2} \). Plugging in these values, we get: \[ y = -\frac{1}{2}x - \frac{1}{2} \] This means that for every 2 units you move to the right, the line drops 1 unit down. Understanding slopes and intercepts can be crucial for interpreting and modeling real-world phenomena, such as predicting costs or analyzing trends. For example, if this line represented cost over time, you could interpret the \( y \)-intercept as the initial cost and the slope as how quickly cost decreases as time goes on. Such insights can help businesses make data-driven decisions!