In Exercises 15–18, write an equation of the line passing through point P that is perpendicular to
the given line. P(4, −6), y = −3

To find the equation of a line that passes through a point and is perpendicular to a given line, follow these steps:

1. **Identify the slope of the given line**:  
   The equation of the given line is \( y = -3 \). This represents a horizontal line, meaning its slope is 0.

2. **Determine the slope of the perpendicular line**:  
   The slope of a line perpendicular to a horizontal line (slope = 0) is undefined, which implies a vertical line.

3. **Equation of the perpendicular line**:  
   A vertical line passing through a point \( P(x_1, y_1) \) has the equation \( x = x_1 \).  
   Since the point \( P(4, -6) \) lies on the perpendicular line, the equation of the line is:
   \[
   x = 4
   \]
   This is the equation of the line perpendicular to \( y = -3 \) and passing through \( P(4, -6) \).

Would you like further clarification on any steps or additional details?

Here are some related questions for practice:
1. What is the equation of a line passing through \( P(2, 3) \) and perpendicular to \( y = 5 \)?
2. Write the equation of a line passing through \( P(0, -2) \) and perpendicular to \( x = -4 \).
3. How do you find the slope of a line perpendicular to a line with slope 2?
4. If a line has slope \( \frac{3}{4} \), what is the slope of the perpendicular line?
5. What is the general form of the equation of a vertical line?

**Tip**: For vertical and horizontal lines, their slopes are special cases. Vertical lines have an undefined slope, and horizontal lines have a slope of 0.

In Exercises 15–18, write an equation of the line passing through point P that is perpendicular to the given line. P(4, −6), y = −3

Learn how to find the equation of a line that is perpendicular to y = -3 and passes through the point P(4, -6). This problem involves understanding perpendicular line slopes and writing the equation of a vertical line. Ideal for students in Grades 8-10.

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