1. **State the problem:** We are given the equation of a line: $$5y = 35 + 6x$$ and need to find the coordinates of its y-intercept. 2. **Recall the y-intercept definition:** The y-intercept is the point where the line crosses the y-axis. At this point, the value of $x$ is 0. 3. **Substitute $x=0$ into the equation:** $$5y = 35 + 6 \times 0$$ $$5y = 35$$ 4. **Solve for $y$:** $$y = \frac{35}{5} = 7$$ 5. **Write the coordinates of the y-intercept:** Since $x=0$ and $y=7$, the y-intercept is at the point $$(0, 7)$$. **Final answer:** The coordinates of the y-intercept are $(0, 7)$.