1. **State the problem:** We are given the equation of a line in the Cartesian plane: $$2 - y = 5 - x$$ and a point on the line with an x-coordinate of $$x = -3$$. We need to find the corresponding y-coordinate. 2. **Rewrite the equation:** Start by isolating $$y$$ in the equation. $$2 - y = 5 - x$$ Subtract 2 from both sides: $$-y = 5 - x - 2$$ Simplify the right side: $$-y = 3 - x$$ Multiply both sides by $$-1$$ to solve for $$y$$: $$y = x - 3$$ 3. **Substitute the given x-coordinate:** Substitute $$x = -3$$ into the equation: $$y = (-3) - 3$$ $$y = -6$$ 4. **Final answer:** The y-coordinate corresponding to $$x = -3$$ on the line is $$y = -6$$.