Question

State whether the pair of equations describes parallel lines,perpendicular lines, or neither and explain.

3x=-y+6, 6y=2x-4x

Answer 1

perpendicular lines

Explanation:

• Parallel lines have equal slopes

• The product of the slopes of perpendicular lines = - 1

the equation of a line in slope- intercept form is

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

given

3x = - y + 6 ( add y to both sides )

y + 3x = 6 ( subtract 3x from both sides )

y = - 3x + 6 ← in slope- intercept form

with slope m = - 3

given

6y = 2x - 4 ( divide through by 6 )

`(6)/(6)` y =
`(2)/(6)` x -
`(4)/(6)` , that is

y =
`(1)/(3)` x -
`(2)/(3)` ← in slope- intercept form

with slope m =
`(1)/(3)`

- 3 ≠
`(1)/(3)` ⇒ lines are not parallel

- 3 ×
`(1)/(3)` ⇒ lines are perpendicular