https://file.aiquickdraw.com/mathbot/file/1725924588304608c2mnt.jpg

In the provided image, the equation of the line is given as:

\[
y = -4 - 5x
\]

This is in the slope-intercept form \(y = mx + b\), where \(m\) is the slope, and \(b\) is the y-intercept. From the equation \(y = -4 - 5x\), we can see that the slope (\(m\)) is \(-5\).

Now, let’s address the questions:

1. **What is the slope of a line parallel to this line?**

   The slope of a parallel line is always the same as the slope of the given line. So, the slope of a parallel line is:
   \[
   \text{slope of parallel line} = -5
   \]

2. **What is the slope of a line perpendicular to this line?**

   The slope of a line perpendicular to another line is the negative reciprocal of the original slope. The reciprocal of \(-5\) is \(\frac{1}{5}\), and the negative reciprocal is:
   \[
   \text{slope of perpendicular line} = \frac{1}{5}
   \]

In the image, it appears there was an error in calculating the slope of the perpendicular line, as it is listed as "4." The correct answer should be \(\frac{1}{5}\).

Would you like further details or clarification?

Here are five related questions:
1. How do you find the equation of a line perpendicular to a given line?
2. What happens to the y-intercept when two lines are parallel?
3. How do you graph a line given its slope and y-intercept?
4. Can two lines with the same slope ever intersect?
5. How do you find the point of intersection between two perpendicular lines?

**Tip:** Always remember that parallel lines have equal slopes, while perpendicular lines have slopes that are negative reciprocals of each other.

What is the slope of a line perpendicular and parallel to the line y = -4 - 5x?

Understand how to find the slopes of lines parallel and perpendicular to the given line y = -4 - 5x. Learn about the slope formula and the concept of negative reciprocal for perpendicular lines. Suitable for Grades 8-10.

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