1. The problem is to graph the linear function $$y = -\frac{1}{3}x + 5$$ and understand its properties. 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 decreases by 1 unit in $y$ for every 3 units increase in $x$. 4. The y-intercept $b = 5$ means the line crosses the y-axis at the point $(0,5)$. 5. To find the x-intercept, set $y=0$ and solve: $$0 = -\frac{1}{3}x + 5$$ $$\frac{1}{3}x = 5$$ $$x = \cancel{3} \times 5 = 15$$ 6. So the x-intercept is at $(15,0)$. 7. The line passes through points $(0,5)$ and $(15,0)$, showing a downward slope. 8. The points $(-6,5)$ and $(6,5)$ mentioned are on the horizontal line $y=5$, which is different from the given function. 9. The graph of $$y = -\frac{1}{3}x + 5$$ is a straight line crossing the y-axis at 5 and sloping downward to the right. Final answer: The function is $$y = -\frac{1}{3}x + 5$$ with slope $-\frac{1}{3}$ and y-intercept 5.