1. The problem is to graph the line given by the equation $$y = \frac{1}{3}x + 7$$ on a Cartesian coordinate grid. 2. The equation is in slope-intercept form $$y = mx + b$$ where $$m$$ is the slope and $$b$$ is the y-intercept. 3. Here, the slope $$m = \frac{1}{3}$$ means the line rises 1 unit for every 3 units it moves to the right. 4. The y-intercept $$b = 7$$ means the line crosses the y-axis at the point $$(0,7)$$. 5. To graph, start at $$(0,7)$$ on the y-axis. 6. From there, use the slope to find another point: move 3 units right (positive x direction) and 1 unit up (positive y direction) to reach $$(3,8)$$. 7. Draw a straight line through these points extending across the grid. 8. This line represents all points $$ (x,y) $$ satisfying $$ y = \frac{1}{3}x + 7 $$. Final answer: The line crosses the y-axis at 7 and rises 1 unit for every 3 units moved right, graphing the equation $$y = \frac{1}{3}x + 7$$.