Question

1. Line a passes through (-2,-5) and (0, -1); Line b passes through (3, 1) and (1, -3).

A. parallel
B. perpendicular
C. neither

Answer 1

keeping in mind that perpendicular lines have negative reciprocal slopes, and that parallel lines have exactly the same slope, let's check for the slope of both.

`(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-1}-\stackrel{y1}{(-5)}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-2)}}} \implies \cfrac{-1 +5}{0 +2} \implies \stackrel{ \textit{\LARGE Line A} }{\cfrac{ 4 }{ 2 } \implies 2} \\\\[-0.35em] ~\dotfill`

`(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-3}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-3}-\stackrel{y1}{1}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{3}}} \implies \stackrel{ \textit{\LARGE Line B} }{\cfrac{ -4 }{ -2 } \implies 2} \\\\\\ ~\hfill~\textit{\LARGE parallel lines}~\hfill~`