1. The problem is to graph the linear function $y = -\frac{1}{3}x + 5$. 2. The formula for a linear function is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. Here, the slope $m = -\frac{1}{3}$ means the line goes down 1 unit for every 3 units it moves to the right. 4. The y-intercept $b = 5$ means the line crosses the y-axis at the point $(0, 5)$. 5. To graph, start at $(0, 5)$ on the y-axis. 6. From there, move down 1 unit and right 3 units to find another point at $(3, 4)$. 7. Draw a straight line through these points extending in both directions. This line represents the function $y = -\frac{1}{3}x + 5$.