1. **State the problem:** We need to write the equation of the line in slope-intercept form. 2. **Recall the slope-intercept form:** The slope-intercept form of a line is given by $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Identify the slope and y-intercept:** From the equation $$y = \frac{2}{3}x + 1$$ we see that the slope $m = \frac{2}{3}$ and the y-intercept $b = 1$. 4. **Interpret the slope:** The slope $\frac{2}{3}$ means that for every 3 units moved horizontally to the right, the line rises 2 units vertically. 5. **Final equation:** The equation is already in slope-intercept form: $$y = \frac{2}{3}x + 1$$ This means the line crosses the y-axis at 1 and rises 2 units for every 3 units it moves to the right along the x-axis.