Question

question 2 of 5
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{q}{p}\\)
\\(\bigcirc\\) c. \\(\frac{q}{p}\\)
\\(\bigcirc\\) d. \\(\frac{p}{q}\\)

Explanation:

Step1: Recall perpendicular slope rule

Perpendicular slopes are negative reciprocals. If a line has slope $m_1$, its perpendicular slope $m_2 = -\frac{1}{m_1}$.

Step2: Substitute given slope

Line m has slope $\frac{p}{q}$. Calculate negative reciprocal:
$m_2 = -\frac{1}{\frac{p}{q}} = -\frac{q}{p}$

Answer:

B. $-\frac{q}{p}$