We start with the given equation of the line:

$5x + y = -4$

Step 1: Convert to Slope-Intercept Form

The slope-intercept form of a line is:

$y = mx + b$

where $m$ is the slope. Solve for $y$:

$y = -5x - 4$

Thus, the slope of the given line is $m = -5$.

Step 2: Find the Perpendicular Slope

The slope of a line perpendicular to another is the negative reciprocal of the given slope. The negative reciprocal of $-5$ is:

$m_{\perp} = \frac{1}{5}$

Final Answer:

The slope of a line perpendicular to the given line is $\frac{1}{5}$.

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Would you like a step-by-step explanation of how negative reciprocals work?

Here are 5 related questions you might find interesting:

1. What is the equation of a line perpendicular to $5x + y = -4$ that passes through (2,3)?
2. How do you find the slope of a parallel line instead of a perpendicular one?
3. If two lines are perpendicular, how do their slopes always relate?
4. Can a vertical line be perpendicular to a horizontal line? Why or why not?
5. What happens if the original line has a slope of 0 or is undefined?

Tip: Always check that the product of perpendicular slopes equals -1 (e.g., $-5 \times \frac{1}{5} = -1$).