1. **Problem Statement:** We need to identify which graph corresponds to the function rule $$y = \frac{x}{3} + 2$$. 2. **Understanding the function:** The function is a linear equation in slope-intercept form $$y = mx + b$$, where $$m$$ is the slope and $$b$$ is the y-intercept. 3. **Identify slope and intercept:** Here, $$m = \frac{1}{3}$$ (positive slope) and $$b = 2$$ (y-intercept). 4. **Interpret the slope:** A positive slope means the line rises as $$x$$ increases. 5. **Check the points given for each graph:** - First graph points: (-3,1), (0,2), (3,3) - Second graph points: (-3,5), (0,2), (3,-1) - Third graph points: (-3,3), (0,2), (3,1) 6. **Verify the function at these points:** - For $$x = -3$$: $$y = \frac{-3}{3} + 2 = -1 + 2 = 1$$ - For $$x = 0$$: $$y = \frac{0}{3} + 2 = 2$$ - For $$x = 3$$: $$y = \frac{3}{3} + 2 = 1 + 2 = 3$$ 7. **Match points to graphs:** The first graph has points (-3,1), (0,2), (3,3), which exactly match the function values. 8. **Conclusion:** The first graph (left side) is the graph of the function $$y = \frac{x}{3} + 2$$ because it has the correct positive slope and y-intercept. **Final answer:** The first graph (left side) represents the function $$y = \frac{x}{3} + 2$$.