Question

line p has a slope of $\frac{5}{8}$. line q is perpendicular to p. what is the slope of line q? simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Recall slope - perpendicular rule

The product of slopes of two perpendicular lines is - 1. Let the slope of line $p$ be $m_1=\frac{5}{8}$ and the slope of line $q$ be $m_2$. Then $m_1\times m_2=-1$.

Step2: Solve for $m_2$

We have $\frac{5}{8}\times m_2=-1$. To find $m_2$, we divide both sides of the equation by $\frac{5}{8}$, which is equivalent to multiplying both sides by $\frac{8}{5}$. So $m_2=-1\div\frac{5}{8}=-1\times\frac{8}{5}=-\frac{8}{5}$.

Answer:

$-\frac{8}{5}$