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-4y=-2x+8 and 3x-6y=6
Perpendicular, parallel, or neither?

User Spinus
by
8.3k points

1 Answer

6 votes

Answer:

The two lines are parallel

Explanation:

  • Parallel lines have equal slopes and different y-intercepts
  • The product of the slopes of the perpendicular lines is -1 which means if the slope of one is m, then the slope of the other is
    -(1)/(m) (reciprocal m and change its sign)
  • The slope of the equation ax + by = c is m =
    (-a)/(b)
  • The slope of the equation by = ax + c is m =
    (a)/(b)

Let us use these rules to solve the question

∵ The 1st equation is -4y = -2x + b

a = -2 and b = -4

∵ m =
(a)/(b) in this form of the equation

∴ m =
(-2)/(-4)

m1 =
(1)/(2)

∵ The 2nd equation is 3x - 6y = 6

a = 3 and b = -6

∵ m =
(-a)/(b) in this form of the equation

∴ m =
(-3)/(-6)

m2 =
(1)/(2)

m1 = m2

∴ The slopes of the two lines are equal

→ That means the two lines are parallel

The two lines are parallel

User Igor Dvorzhak
by
7.3k points

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