1. The problem is to graph the line given by the equation $$y = \frac{2}{3}x + 1$$. 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 $$m = \frac{2}{3}$$ and the y-intercept $$b = 1$$. 4. The y-intercept means the line crosses the y-axis at the point $$(0,1)$$. 5. To graph the line, start at $$(0,1)$$ on the y-axis. 6. Use the slope $$\frac{2}{3}$$ which means rise 2 units up and run 3 units right from the y-intercept to find another point. 7. Plot the point $$(3, 3)$$ because starting at $$(0,1)$$ and moving 3 units right and 2 units up gives $$(0+3, 1+2) = (3,3)$$. 8. Draw a straight line through the points $$(0,1)$$ and $$(3,3)$$. 9. This line represents the equation $$y = \frac{2}{3}x + 1$$. Final answer: The line passes through $$(0,1)$$ and has slope $$\frac{2}{3}$$.