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Sagot :

Answer:

see explanation

Step-by-step explanation:

(3)

Parallel lines have equal slopes

the equation of a line in sloipe- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{4}[/tex] x + 5 ⇒ m = [tex]\frac{1}{4}[/tex]

y = 4x + 5 ⇒ m = 4

y = - 4x + 5 ⇒ m = - 4

y = - 4x - 9 ⇒ m = - 4

the 3rd and 4th options have equal slopes and are parallel

(4)

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex]

y = [tex]\frac{1}{6}[/tex] x + 4 ⇒ m = [tex]\frac{1}{6}[/tex]

y = - [tex]\frac{1}{6}[/tex] x + 5 ⇒ m = - [tex]\frac{1}{6}[/tex]

y = [tex]\frac{1}{6}[/tex] x + 3 ⇒ m = [tex]\frac{1}{6}[/tex]

y = 6x + 3 ⇒ m = 6

note that a slope of m = 6 , has a perpendicular slope of

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{6}[/tex]

the 2nd and 4th lines are perpendicular

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