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.