Writing Equations of Parallel Lines

When lines are parallel, their slopes are the same. To find out if Ron-Jon's walls are parallel, we first have to find the slopes of the segments that connect each pair of points. Once we have the slopes, we can compare them to see if they are parallel or not.

Wall 1

Let's substitute the coordinates of the points $(1,2)$ and $(4,3)$ into the slope formula. $\begin{gathered} m = \dfrac{y_2-y_1}{x_2-x_1} \end{gathered}$ This way, we can determine the slope of the line that represents wall $1.$ Thus, wall $1$ has the slope $\frac{1}{3}.$

Wall 2

Once again, we'll substitute the coordinates of the points that maps wall $2$ into the slope formula. Thus, wall $2$ has slope $\frac{3}{2}.$

Comparing slopes

Unfortunately the slopes aren't equal. $\frac{1}{3}\neq\frac{3}{2}$ Hence, the walls are not parallel.