1. **State the problem:** We need to write the equation of a line in slope-intercept form given the slope and y-intercept. 2. **Recall the slope-intercept form:** The equation of a line is given by $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Substitute the given values:** Here, slope $m = 2$ and y-intercept $b = 1$. 4. **Write the equation:** Substituting these values into the formula, we get $$y = 2x + 1$$. 5. **Interpretation:** This means the line crosses the y-axis at 1 and rises 2 units vertically for every 1 unit it moves horizontally to the right. **Final answer:** $$y = 2x + 1$$