1. **State the problem:** Write the slope-intercept form of the equation of the line given the slope and y-intercept. 2. **Recall the slope-intercept form:** The equation of a line in slope-intercept form is given by $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Apply the formula to the first problem:** Given slope $m = 1$ and y-intercept $b = 3$, substitute these values into the formula: $$y = 1x + 3$$ 4. **Simplify the equation:** Since $1x$ is just $x$, the equation simplifies to $$y = x + 3$$ This is the slope-intercept form of the line with slope 1 and y-intercept 3. **Final answer:** $$y = x + 3$$