Answer:
[tex]L_{1}[/tex] ⊥ [tex]L_{2}[/tex] ; [tex]L_{3}[/tex] ⊥ [tex]L_{2}[/tex] ; [tex]L_{1}[/tex] ║ [tex]L_{3}[/tex]
Step-by-step explanation:
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
y = mx + b
"m" is slope
"b" is y-intercept (coordinates are (0, b)
Parallel lines have the same slopes and different y-intercepts.
Slopes of perpendicular lines are opposite reciprocals: [tex]m_{1}[/tex] × [tex]m_{2}[/tex] = - 1
~~~~~~~~~~~~~~~~~~~~~~
[tex]L_{1}[/tex] : y = x + 5 , [tex]m_{L_{1} }[/tex] = 1 , b = 5
[tex]L_{2}[/tex] : y = - x + 7 , [tex]m_{L_{2} }[/tex] = - 1 , b = 7
[tex]L_{1}[/tex] ⊥ [tex]L_{2}[/tex]
[tex]L_{3}[/tex] : [tex]m_{L_{3} }[/tex] = 1 , b = - 2
[tex]L_{1}[/tex] ║ [tex]L_{3}[/tex] and [tex]L_{2}[/tex] ⊥ [tex]L_{3}[/tex]
