Find the y-intercept of the line with the equation \( y = -\frac{1}{2}x + 5 \).

To find the y-intercept of the line given by the equation \( y = -\frac{1}{2}x + 5 \), you simply need to determine the value of \( y \) when \( x = 0 \). Plugging \( 0 \) into the equation gives you: \[ y = -\frac{1}{2}(0) + 5 = 5. \] So, the y-intercept is \( 5 \), which means the line crosses the y-axis at the point \( (0, 5) \). Now, let’s put a little context around it! The y-intercept can be viewed as the starting point of your line on the Cartesian plane, and each point on the line is determined by the slope of \( -\frac{1}{2} \), which means for every 2 units you move to the right along the x-axis, you will move down 1 unit along the y-axis. This downward trend also tells you something about the relationship you're modeling – it could be something like a decreasing profit over time if you think economically! To deepen your understanding, consider this: if you're graphing a linear equation, knowing the y-intercept is essential. It allows you to sketch the line quickly. Just mark the point \( (0, 5) \) on the graph, and from there, use the slope to find another point. For instance, if you go 2 units right to \( x = 2 \), then drop down 1 unit to \( y = 4 \) to locate another point. Connecting the dots gives you the line! Graphing equations is not just about the math; it's about visualizing relationships creatively.