Question

The equations of three lines are given below.

Line 1: 2y = 3x+7
Line 2: 4x-6y=-2
3
Line 3: y==x-4
For each pair of lines, determine whether they are parallel, perpendicular, or neither.
Line 1 and Line 2:
O Parallel
O Perpendicular O Neither
Х
?
Line 1 and Line 3: O Parallel O Perpendicular ONeither
Line 2 and Line 3:
O Parallel Operpendicular ONeither

Answer 1

a) Neither

b) parallel

Two slopes are L₁ and L₃ is equal

∴ L₁ and L₃ are parallel lines

c) neither

Explanation:

Step(i):-

Given that the Line 1

2 y = 3x+7

`y = (3)/(2) x+(7)/(2)` ...(i)

comparing y = m x +c

here
`m = (3)/(2)`

Given that the Line 2

4x-6y =-2

4x +2 =6y

`y = (4)/(6) x + (2)/(6)`

`y = (2)/(3) x + (1)/(3)` ...(ii)

m =
`(2)/(3)`

The two lines are not parallel or perpendicular

Step(ii):-

Given that line 3

`y = (3)/(2) x -4` ...(iii)

here
`m = (3)/(2)`

Two slopes are L₁ and L₃ is equal

∴ L₁ and L₃ are parallel lines

Step(iii):-

`y = (2)/(3) x + (1)/(3)` ...(ii)

`y = (3)/(2) x -4` ...(iii)

L₂ and L₃ arenot parallel lines and not perpendicular