Certainly! To find the equation of a line that passes through a given point and is perpendicular to another line, follow these steps:
1. **Understand the given line**: We are given the line y = -7. This is a horizontal line because it has the form y = some constant. A horizontal line has a slope of 0.
2. **Determine the slope of the perpendicular line**: Lines that are perpendicular to each other have slopes that are negative reciprocals of one another. Since a horizontal line has a slope of 0, the negative reciprocal of 0 would be undefined. Thus, a line perpendicular to a horizontal line is a vertical line.
3. **Equation of a vertical line**: The general equation of a vertical line is x = a constant, where the constant is the x-coordinate of any point the line goes through.
4. **Apply the given point**: We need the line to pass through the point (-3, -8). For a vertical line, we don't need to worry about the y-coordinate since the line will pass through all points that have the x-coordinate of -3.
Hence, the equation of the line that passes through the point (-3, -8) and is perpendicular to the line y = -7 is x = -3.