How do you determine if the lines through the given points (3,2), (5,8) are parallel and which, if any, are perpendicular?

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Answer 1 · 2018-07-27T13:38:53

See hint below

HINT:

The slope #m# of the line parallel to the line passing through the given points #(x_1, y_1)\equiv(3, 2)# & #(x_2, y_2)\equiv(5, 8)# is given as

#m=\frac{y_2-y_1}{x_2-x_1}#

#=\frac{8-2}{5-3}#

#=3#

The slope #m# of the line perpendicular to the line passing through the given points #(x_1, y_1)\equiv(3, 2)# & #(x_2, y_2)\equiv(5, 8)# is given as

#m=-{1}/{\frac{y_2-y_1}{x_2-x_1}}#

#=-1/\frac{8-2}{5-3}#

#=-1/3#