Question

Given the points below, are the two lines parallel, perpendicular, or neither.

L1: (-3,-4) (-5,2) L2: (1, -6) (-2,3)

Answer 1

Parallel

Explanation:

Calculate the slope m of the lines using the slope formula.

If the slopes are equal then the lines are parallel

If the product of the slopes is - 1 then the lines are perpendicular.

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (- 3, - 4) and (x₂, y₂ ) = (- 5, 2)

m =
`(2+4)/(-5+3)` =
`(6)/(-2)` = - 3 ← slope of L1

Repeat with (x₁, y₁ ) = (1, - 6) and (x₂, y₂ ) = (- 2, 3)

m =
`(3+6)/(-2-1)` =
`(9)/(-3)` = - 3 ← slope of L2

Since the slopes are equal then the two lines are parallel

Answer 2

The given lines are parallel when plotted in graph.

Explanation: