Question

Which two lines are parallel?
Which two lines are perpendicular?

Answer 1

see explanation

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 )

All the equations given are in slope- intercept form

y = 2x + 1 → with m = 2

y =
`(1)/(2)` x - 4 → with m =
`(1)/(2)`

y = x + 1 → with m = 1

y = -
`(1)/(x)` x - 3 → with m = -
`(1)/(2)`

y = 10 + x → y = x + 10 → with m = 1

Thus

y = x + 1 and y = 10 + x are Parallel since both have m = 1

y = 2x + 1 and y = -
`(1)/(2)` x - 3 are Perpendicular since 2 × -
`(1)/(2)` = - 1