1. **State the problem:** We are given the equation of a line $$y + 4 = 6x + 11$$ and asked to find the y-intercept of the line. 2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $$y = mx + b$$ where $$b$$ is the y-intercept. 3. **Isolate $$y$$:** $$y + 4 = 6x + 11$$ Subtract 4 from both sides: $$y + \cancel{4} - \cancel{4} = 6x + 11 - 4$$ $$y = 6x + 7$$ 4. **Identify the y-intercept:** The y-intercept $$b$$ is the constant term when $$x=0$$. 5. **Final answer:** $$\boxed{7}$$ is the y-intercept of the line. This means the line crosses the y-axis at the point $$(0,7)$$.