Find the equation for the line that passes through the point (2,−2), and that is perpendicular to the line with the equation y=2.

To find the equation of the line that is perpendicular to the line \( y = 2 \) and passes through the point \( (2, -2) \), we need to consider the following steps:

### 1. Analyze the given line \( y = 2 \):
The equation \( y = 2 \) represents a **horizontal line** at \( y = 2 \). The slope of a horizontal line is 0.

### 2. Slope of the perpendicular line:
A line that is **perpendicular** to a horizontal line must be a **vertical line**. Vertical lines have undefined slopes and are described by equations of the form \( x = c \), where \( c \) is the x-coordinate of every point on the line.

### 3. Equation of the perpendicular line:
Since the line is vertical and passes through the point \( (2, -2) \), its equation is simply:
\[
x = 2
\]

### Final Answer:
The equation of the line that passes through \( (2, -2) \) and is perpendicular to the line \( y = 2 \) is:
\[
x = 2
\]

Would you like more details on any part of this solution?

Here are 5 related questions to explore further:
1. What is the equation of a line parallel to \( y = 2 \) that passes through \( (1, 3) \)?
2. How would you find the equation of a line perpendicular to \( x = 5 \)?
3. Can you determine the slope of a line perpendicular to a line with slope 3?
4. How do you find the equation of a line passing through two points?
5. What is the equation of a line parallel to the y-axis?

**Tip:** A line perpendicular to a horizontal line is always vertical, and a line perpendicular to a vertical line is always horizontal.

Learn how to find the equation of a line perpendicular to y = 2 that passes through the point (2, -2). This solution covers the concept of perpendicular lines, vertical line equations, and theorems related to line slopes. Suitable for students in Grades 8-10.

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