Respuesta :

Answer:

The two lines are parallel

Step-by-step 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 [tex]-\frac{1}{m}[/tex] (reciprocal m and change its sign)
  • The slope of the equation ax + by = c is m = [tex]\frac{-a}{b}[/tex]
  • The slope of the equation by = ax + c is m = [tex]\frac{a}{b}[/tex]

Let us use these rules to solve the question

∵ The 1st equation is -4y = -2x + b

a = -2 and b = -4

∵ m = [tex]\frac{a}{b}[/tex] in this form of the equation

∴ m = [tex]\frac{-2}{-4}[/tex]

m1 = [tex]\frac{1}{2}[/tex]

∵ The 2nd equation is 3x - 6y = 6

a = 3 and b = -6

∵ m = [tex]\frac{-a}{b}[/tex] in this form of the equation

∴ m = [tex]\frac{-3}{-6}[/tex]

m2 = [tex]\frac{1}{2}[/tex]

m1 = m2

∴ The slopes of the two lines are equal

→ That means the two lines are parallel

The two lines are parallel