1. **State the problem:** We need to sketch the graph of a line with slope $2$ and y-intercept $3$. 2. **Recall the formula:** The equation of a line in slope-intercept form is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Substitute the given values:** Here, $m = 2$ and $b = 3$, so the equation is $$y = 2x + 3$$. 4. **Plot the y-intercept:** Start by plotting the point where the line crosses the y-axis, which is at $(0, 3)$. 5. **Use the slope to find another point:** The slope $2$ means rise over run is $2/1$. From $(0, 3)$, move up $2$ units and right $1$ unit to reach the point $(1, 5)$. 6. **Draw the line:** Connect the points $(0, 3)$ and $(1, 5)$ with a straight line extending in both directions. This is how you sketch the graph of the line with slope $2$ and y-intercept $3$.