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

To find the y-intercept of a line, we simply set \( x = 0 \) in the equation. Plugging in \( x = 0 \) into the equation \( y = -\frac{1}{2}(0) + 5 \), we get \( y = 5 \). Therefore, the y-intercept is \( (0, 5) \). The y-intercept is the point where the line crosses the y-axis, and in this case, it’s located at 5 units above the origin. Visualizing this can be fun: imagine you're a tiny critter climbing up a vertical line, and when you reach that point, you find a beautifully scenic view at \( (0, 5) \)! Now, have you ever considered that every line can be graphed, and these intercepts can often guide us? When you graph \( y = -\frac{1}{2}x + 5 \), you’ll see that it flows downward from the y-intercept. This means it’s a linear equation with a negative slope, indicating a relationship where as x increases, y decreases. You can actually plot it to see how it behaves across different values!