Question

The line L passes through the points (-2, 1) and (2, 3). The line N passes through the points (4, 7) and (12, 11). Bryan says that the lines L and N are parallel. Is Bryan correct? Explain your answer.​

Answer 1

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of each line, let's see if that's true.

`(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{1}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{(-2)}}} \implies \cfrac{ 2 }{2 +2} \implies \cfrac{ 2 }{ 4 } \implies \cfrac{1}{2}\qquad \impliedby \textit{\LARGE Line L} \\\\[-0.35em] ~\dotfill`

`(\stackrel{x_1}{4}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{11}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{11}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{12}-\underset{x_1}{4}}} \implies \cfrac{ 4 }{ 8 } \implies \cfrac{1}{2}\qquad \impliedby \textit{\LARGE Line N}\quad \textit{Bryan is Da Man!}`