Beginning Algebra With Applications, Chapter 5, 5.3, Section 5.3, Problem 32

Is the line containing the points $(4,-3)$ and $(2,5)$ parallel to the line that contains the points $(-2,-3)$ and $(-4,1)$?

We find the slope of the line through $(4,-3)$ and $(2,5)$

Using Slope Formula,


$
\begin{equation}
\begin{aligned}

m =& \frac{5-(-3)}{2-4}
\\
\\
m =& \frac{5+3}{-2}
\\
\\
m =& \frac{8}{-2}
\\
\\
m =& -4

\end{aligned}
\end{equation}
$


We find the slope of the line through $(-2,-3)$ and $(-4,1)$

Using Slope Formula,


$
\begin{equation}
\begin{aligned}

m =& \frac{1-(-3)}{-4-(-2)}
\\
\\
m =& \frac{1+3}{-4+2}
\\
\\
m =& \frac{4}{-2}
\\
\\
m =& -2

\end{aligned}
\end{equation}
$


The slopes of the two lines are different so they are not parallel to one another.