Question

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

Explanation:

Step1: Recall perpendicular slope rule

Perpendicular slopes multiply to $-1$. Let original slope $m_1=\frac{p}{q}$.

Step2: Solve for new slope $m_2$

$m_1 \times m_2 = -1 \implies m_2 = -\frac{q}{p}$

Answer:

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