Question

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

Answer 1

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 $-\frac{1}{m}$ (reciprocal m and change its sign)

• The slope of the equation ax + by = c is m = $\frac{-a}{b}$

• The slope of the equation by = ax + c is m = $\frac{a}{b}$

Let us use these rules to solve the question

∵ The 1st equation is -4y = -2x + b

∴ a = -2 and b = -4

∵ m = $\frac{a}{b}$ in this form of the equation

∴ m = $\frac{-2}{-4}$

∴ m1 = $\frac{1}{2}$

∵ The 2nd equation is 3x - 6y = 6

∴ a = 3 and b = -6

∵ m = $\frac{-a}{b}$ in this form of the equation

∴ m = $\frac{-3}{-6}$

∴ m2 = $\frac{1}{2}$

∵ m1 = m2

∴ The slopes of the two lines are equal

→ That means the two lines are parallel

∴ The two lines are parallel