Are my answers correct?

Question

Identify which lines are parallel.

1. y = 6; y = 6x + 5; y = 6x - 7; y = -8

A: y = 6; y = -8; y = 6x +5; y = 6x - 7 (all)

2. y = 3/4x - 1; y = -2x; y - 3 = 3/4(x - 5); y - 4 = -2(x + 2)

A: y = 3/4x - 1; y- 3 = 3/4(x -5)

Identify which lines are perpendicular.

3. y = 2/3x - 4; y = -3/2x + 2; y = -1; x = 3

A: y = 2/3x - 4; y = -3/2x + 2; y = -1; x = 3 (all)

4. y = -3/7x - 4; y - 4 = -7(x + 2); y - 1 = 1/7(x - 4); y - 7 = 7/3(x - 3)

A: y = -3/7x - 4; y - 4 = -7(x + 2); y - 1 = 1/7(x - 4); y - 7 = 7/3(x - 3) (all)

5. Show that PQRS is a rectangle.
(P: (1,4); Q: (2,6); R: (8,3); S: (7,1)

A: PQ is perpendicular to QR because 2(-1/2) = -1. RS is perpendicular to PS because 2(-1/2) = -1. Therefore. RQRS is a rectangle because it contains a right angle.

Answer 1

1. y=6 and y=-8 are parallel, they are both horizontal
y=6x + 5 and y = 6x-7 are parallel, they both have a slope of 6

2. the first and third are parallel, you had that
but also the 2nd and last line are parallel, both have a slope of -2

3. the 1st and 2nd lines are perpendicular
the last two , y = -1, and x=3 are perpendicualar.
The y = -1 is horizontal, x=3 is vertical

4. 1st and last, as well as the 2nd and third

5.You have shown that opposite angles are 90° each, but I can draw a quad where opposite angles are each 90° , one other is 80, and the third is 100
so you have to show one more vertex to have a 90°
(Then 3 90's would leave 90 for the fourth angle)

Answer 2

Can someone please tell me whether these answers are correct or not?

Answer 3

5. I don't quite understand what you said. Have I answered correctly?

Answer 4

#5.
no, it is not a rectangle.
angle P = 90°
angle S = 90°

but since slope PQ = 2 and slope of QR = -3/5
we don't have a right angle at Q

no need to go further.

Answer 5

But I thought PQ = -1/2.

Answer 6

Oh. It appears that I have made a mistake.

Correction: But I thought that QR = -1/2.