1. The problem is to analyze the linear function given by the equation $y = -\frac{1}{2}x + 3$. 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 1 unit in $y$ for every 2 units increase in $x$. 4. The y-intercept $b = 3$ means the line crosses the y-axis at the point $(0, 3)$. 5. To find the x-intercept, set $y=0$ and solve for $x$: $$0 = -\frac{1}{2}x + 3$$ $$\frac{1}{2}x = 3$$ $$x = 6$$ So the x-intercept is at $(6, 0)$. 6. The line has no extrema (no maximum or minimum points) because it is linear. 7. Summary: - Slope: $-\frac{1}{2}$ - Y-intercept: $(0, 3)$ - X-intercept: $(6, 0)$ This line decreases gently from left to right crossing the y-axis at 3 and the x-axis at 6.