Question

A line contains points (2, -2) and (-4, 1). Another line graphed in the same coordinate plane contains points (1, 2) and (-3, 4). Based on the slopes of these lines, are they parallel, perpendicular or neither?

Answer 1

Find the slope.
\[Slope = \frac{ y2 - y2 }{ x2 - x1}\]

(2, -2) and (-4, 1):
\[slope = \frac{ 1 -(-2) }{(-4) - 2 } = \frac{ 1 + 2 }{(-4) - 2 } = \frac{ 3 }{ -6 } =-\frac{ 1 }{ 2 } \]Slope is -1/2


(1, 2) and (-3, 4):
\[slope = \frac{ 4 - 2 }{ (-3) - 1 } = \frac{ 2 }{ -4 } = -\frac{1 }{ 2 }\]Slope is -1/2


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Parallel lines have the same slope
Slope of Perpendicular lines is opposite-reciprocal.

Answer 2

So, based on the slopes of these lines, are they parallel, perpendicular or neither?