1. **Stating the problem:** Find the slope of lines parallel and perpendicular to the x-axis and y-axis. 2. **Recall definitions:** - Lines parallel to the x-axis are horizontal lines with slope $0$. - Lines perpendicular to the x-axis are vertical lines with undefined slope. - Lines parallel to the y-axis are vertical lines with undefined slope. - Lines perpendicular to the y-axis are horizontal lines with slope $0$. 3. **Answering each question:** - Slope of a line parallel to the x-axis: $0$ - Slope of a line perpendicular to the x-axis: undefined - Slope of a line parallel to the y-axis: undefined - Slope of a line perpendicular to the y-axis: $0$ 4. **Explanation:** Horizontal lines have no vertical change, so slope $= \frac{\Delta y}{\Delta x} = 0$. Vertical lines have no horizontal change, so slope $= \frac{\Delta y}{0}$ which is undefined. **Final answers:** - Parallel to x-axis: slope $0$ - Perpendicular to x-axis: slope undefined - Parallel to y-axis: slope undefined - Perpendicular to y-axis: slope $0$