The equations of three lines are given below. line 1: y=-2/3x-4 line 2: 3y=-2x+5 line 3: 3y=-2x+5 for each pair of lines, determine whether they are parallel, perpendicular, or neither.

You are given the equations of three lines are given below.
Line 1:y=-2/3x-4
Line 2: 3y=-2x+5
Line 3: 3y=-2x+5
And you are asked to determine whether they are parallel, perpendicular, or neither.

Line 1 and 2 is parallel because the slopes are equal. Line 1 and 3 is also parallel because the slopes are equal. Line 2 and 3 is also parallel because the slopes are equal.

    for the right-hand side, use cosine double angle identity which states that  cos 2x = cos²x - sin² x    for the left-hand side    we factor using difference of squares.recall difference of squares factoring: a² - b² = (a - b)(a + b)but here we have a⁴ - b⁴, so  a⁴  - b⁴ = (a² - b²)(a²  + b²)note that cos⁴ x is equivalent to (cos x)⁴ and etc.    note that cos²x + sin²x = 1 via the pythagorean identity