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.