Intermediate Algebra, Chapter 3, 3.2, Section 3.2, Problem 74

State whether the lines with equation $2x + y = 6$ and $x - y = 4$ is parallel, perpendicular, or neither.

We find the slope of each line by solving each equation for $y$

Equation 1


$
\begin{equation}
\begin{aligned}

2x + y =& 6
&& \text{Given equation}
\\
y =& -2x + 6
&& \text{Subtract each side by $2x$}

\end{aligned}
\end{equation}
$


Equation 2


$
\begin{equation}
\begin{aligned}

x - y =& 4
&& \text{Given equation}
\\
-y =& - x + 4
&& \text{Subtract each side by $x$}
\\
y =& x - 4
&& \text{Divide each side by $-1$}
\\
y =& 1x - 4
&& \text{Identity Property}

\end{aligned}
\end{equation}
$


We know that the slope is given by the coefficient of $x$ and since the slopes are not equal and not equal to $-1$, the lines are neither parallel nor perpendicular.