https://file.aiquickdraw.com/mathbot/file/1730064454866m7etx272.jpg

Let's walk through the problem shown in the image.

### Problem:
You are asked to find the **equation and slope** of a line that is **perpendicular to** the line \(x = -4\) and passes through a certain point (though the point isn't shown in the cropped image). 

### Step-by-step solution:

1. **Line \(x = -4\)** is a vertical line.  
   - A vertical line has **undefined slope**.

2. **Perpendicular line to a vertical line** will be **horizontal**.  
   - A horizontal line always has a **slope of 0**.

3. **General form of a horizontal line**:  
   - A horizontal line passing through a point \((a, b)\) has the equation \(y = b\).  
   - We would need the specific **y-coordinate of the point** it passes through to complete the equation.

4. **Answer structure**:
   - **Slope**: 0 (because the new line is horizontal).  
   - **Equation**: \(y = b\), where \(b\) is the y-coordinate of the given point.

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If you provide the point where the perpendicular line should pass through, I can finalize the equation for you!

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### Follow-up questions:
1. What is the slope of a vertical line, and why is it undefined?
2. How do perpendicular lines relate in terms of their slopes?
3. What happens to the slope when two lines are parallel?
4. How can you find the equation of a line if both a point and slope are given?
5. What is the equation of a line if the slope is zero?

**Tip:** Always remember that horizontal lines have slopes of zero and their equations are in the form \(y = \text{constant}\).

Find the equation and slope of a line that is perpendicular to the line x = -4 and passes through a specific point.

Learn how to find the equation and slope of a line that is perpendicular to the line x = -4 and passes through a given point. This problem explains key concepts in coordinate geometry, including horizontal and vertical lines, and the slope of perpendicular lines. Suitable for Grades 8-10.

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