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Writing Equations of Parallel Lines

Writing Equations of Parallel Lines 1.14 - Solution

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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)(1,2) and (4,3)(4,3) into the slope formula. m=y2y1x2x1\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 1.1.
m=y2y1x2x1m=\dfrac{y_2-y_1}{x_2-x_1}
m=2314m=\dfrac{{\color{#0000FF}{2}}-{\color{#009600}{3}}}{{\color{#0000FF}{1}}-{\color{#009600}{4}}}
Evaluate right-hand side
m=-1-3m=\dfrac{\text{-} 1}{\text{-} 3}
m=13m=\dfrac{1}{3}
Thus, wall 11 has the slope 13.\frac{1}{3}.

Wall 2

Once again, we'll substitute the coordinates of the points that maps wall 22 into the slope formula.
m=y2y1x2x1m = \dfrac{y_2-y_1}{x_2-x_1}
m=1457m = \dfrac{{\color{#0000FF}{1}}-{\color{#009600}{4}}}{{\color{#0000FF}{5}}-{\color{#009600}{7}}}
Evaluate right-hand side
m=-3-2m=\dfrac{\text{-}3}{\text{-}2}
m=32m=\dfrac{3}{2}
Thus, wall 22 has slope 32.\frac{3}{2}.

Comparing slopes

Unfortunately the slopes aren't equal. 1332 \frac{1}{3}\neq\frac{3}{2} Hence, the walls are not parallel.