Precalculus, Chapter 1, 1.3, Section 1.3, Problem 104

Determine if lines $\displaystyle y = \frac{1}{2}x - 3$ and $y = -2x + 4$ are parallel, perpendicular or either.

We know that if the two lines are parallel, then it should have the same slopes and if the two lines are perpendicular, then the product of their slopes is $-1$. In this case, the slopes are not the same so there are not parallel. But if we multiply the two slopes, we have


$
\begin{equation}
\begin{aligned}

m_1 =& \frac{1}{2} \text{ and } m_2 = -2
\\
m_1 m_2 =& -1
\\
\frac{1}{2} \cdot -2 =& -1
\\
-1 =& -1

\end{aligned}
\end{equation}
$


So the two lines are perpendicular.