Question

3
line m has a y-intercept of c and a slope of \\(\frac{p}{q}\\), where \\(p > 0\\), \\(q > 0\\), and \\(p \
eq q\\).
what is the slope of a line that is perpendicular to line m?
\\(\bigcirc\\) a. \\(-\frac{p}{q}\\)
\\(\bigcirc\\) b. \\(\frac{p}{q}\\)
\\(\bigcirc\\) c. \\(-\frac{q}{p}\\)
\\(\bigcirc\\) d. \\(\frac{q}{p}\\)

Explanation:

Step1: Recall the perpendicular slope rule

The slope of a line perpendicular to a line with slope \( m \) is the negative reciprocal of \( m \), i.e., \( -\frac{1}{m} \).

Step2: Apply the rule to the given slope

The slope of line \( m \) is \( \frac{p}{q} \). So, the slope of the line perpendicular to line \( m \) is the negative reciprocal of \( \frac{p}{q} \), which is \( -\frac{q}{p} \).

Answer:

C. \( -\frac{q}{p} \)