Question

given the line that passes by the point (4, -4) and has slope \\(\frac{1}{5}\\), find the slope of a line that is perpendicular to it.
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Explanation:

Step1: Recall the rule for perpendicular slopes

The slopes of two perpendicular lines are negative reciprocals of each other. That is, if the slope of one line is \( m \), the slope of the line perpendicular to it is \( -\frac{1}{m} \).

Step2: Identify the given slope

The given slope of the line is \( m = \frac{1}{5} \).

Step3: Calculate the perpendicular slope

Using the rule from Step 1, the slope of the line perpendicular to it is \( -\frac{1}{\frac{1}{5}} \). Simplifying this, we know that dividing by a fraction is the same as multiplying by its reciprocal, so \( -\frac{1}{\frac{1}{5}} = -1\times5 = -5 \).

Answer:

\( -5 \)