Question

lines p and q are perpendicular. the slope of line p is \\(\frac{1}{4}\\). which equation is true? \\(-4 \cdot \text{slope of } q = -1\\) \\(-\frac{1}{4} \cdot \text{slope of } q = -1\\) \\(4 \cdot \text{slope of } q = -1\\) \\(\frac{1}{4} \cdot \text{slope of } q = -1\\)

Explanation:

Step1: Recall perpendicular slopes rule

The product of slopes of two perpendicular lines is $-1$. Let $m_p$ = slope of $p$, $m_q$ = slope of $q$. So $m_p \cdot m_q = -1$.

Step2: Substitute known slope of p

Given $m_p = \frac{1}{4}$, substitute into the equation:
$\frac{1}{4} \cdot m_q = -1$

Step3: Verify correct equation match

Compare with the options: the equation $\frac{1}{4} \cdot \text{slope of } q = -1$ matches the derived relationship.

Answer:

$\frac{1}{4} \cdot \text{slope of } q = -1$