To find the slope of a line perpendicular to the line given by the equation:

$5x + y = -4$

we first need to rewrite the equation in slope-intercept form, $y = mx + b$, where $m$ represents the slope.

Step 1: Rewrite the equation in slope-intercept form

Starting with: $5x + y = -4$

Subtract $5x$ from both sides: $y = -5x - 4$

Now, the equation is in slope-intercept form, where the slope $m$ of this line is $-5$.

Step 2: Find the slope of the perpendicular line

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

$\frac{1}{5}$

Final Answer

The slope of the line perpendicular to the given line is:

$\frac{1}{5}$

Would you like further details or have any questions?

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Here are some related questions:

1. How do we determine the equation of a line given a point and a slope?
2. What is the slope of a line parallel to the given line?
3. How do we find the y-intercept in slope-intercept form?
4. What is the relationship between perpendicular slopes?
5. Can you explain the steps to convert to slope-intercept form?

Tip: Remember, perpendicular slopes are always negative reciprocals of each other.