1. The problem is to analyze the linear function given by the equation $y = -\frac{1}{2}x + 4$. 2. This is a linear equation in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. Here, the slope $m = -\frac{1}{2}$ means the line decreases by 0.5 units in $y$ for every 1 unit increase in $x$. 4. The y-intercept $b = 4$ means the line crosses the y-axis at the point $(0,4)$. 5. To find the x-intercept, set $y=0$ and solve for $x$: $$0 = -\frac{1}{2}x + 4$$ 6. Rearranging: $$\frac{1}{2}x = 4$$ 7. Multiply both sides by 2: $$\cancel{2} \times \frac{1}{2}x = \cancel{2} \times 4 \Rightarrow x = 8$$ 8. So the x-intercept is at $(8,0)$. 9. The line passes through $(0,4)$ and $(8,0)$, confirming the slope and intercepts. 10. The negative slope indicates the line goes downwards from left to right, consistent with the graph description. Final answer: The line $y = -\frac{1}{2}x + 4$ has slope $-\frac{1}{2}$, y-intercept at $(0,4)$, and x-intercept at $(8,0)$.