Out of 30 questions these few I struggled with. I put what I feel was right but to be sure I would like some one to check my answers and if there wrong redirect me on how to get the correct answer.( after the = is the answer i think it is.

1.) Given points A(-4, 5), B(2, 3), C(0, 4) and D(5, 0), decide if AB and CD are parallel, perpendicular or neither.
=Neither

2.)Given the equations y = 1x + 7 and y = 3x - 2, decide whether the lines are parallel, perpendicular or neither.
=neither

3.) Given the equations y = 4/3x - 3 and y = -3/4x + 2, decide whether the lines are parallel, perpendicular, or neither.
=Perpendicular

4.) Which set of points are collinear?{options being A(-1,5); B(2,6); C(4,7), A(0,0); B(1/2,3); C(1,5), A(-4,-2); B(0,-4); C(2,-5)
= A(-4,-2); B(0,-4); C(2,-5)

5.) Choose whether the lines given below are parallel, perpendicular or neither.4x - 6y = 9; 3y - 2x = 7j
= neither

6.) Choose whether the lines given below are parallel, perpendicular or neither.
4x - 6y = 9; 4y + 6x = 12
=perpendicular

7.) Choose whether the lines given below are parallel, perpendicular or neither.4x - 6y = 9; 3x - 2y = 11
=neither

8.) Triangle ΔABC has vertices A(2,5), B(8,1) and C(-2,-1) and is a right triangle. If the slope of AB is -2/3 and the slope of AC is 3/2, are the lines parallel, perpendicular or neither?
=perpendicular

3x=6

1.) To determine if AB and CD are parallel, perpendicular, or neither, you can use the slope formula. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1).

For AB:
Slope of AB = (3 - 5) / (2 - (-4))
= -2 / 6
= -1/3

For CD:
Slope of CD = (0 - 4) / (5 - 0)
= -4 / 5

If the slopes are equal, the lines are parallel. If the slopes are negative reciprocals of each other, the lines are perpendicular. Otherwise, they are neither.

In this case, the slopes of AB and CD are not equal, and they are not negative reciprocals of each other. Therefore, the lines AB and CD are neither parallel nor perpendicular.

2.) To determine if the lines y = x + 7 and y = 3x - 2 are parallel, perpendicular, or neither, compare their slopes. The equations are in slope-intercept form, y = mx + b, where m is the slope.

The slope of the first equation y = x + 7 is 1.
The slope of the second equation y = 3x - 2 is 3.

Since the slopes are not equal, the lines are not parallel. Also, the slopes are not negative reciprocals, so the lines are not perpendicular. Therefore, the lines y = x + 7 and y = 3x - 2 are neither parallel nor perpendicular.

3.) To determine if the lines y = (4/3)x - 3 and y = (-3/4)x + 2 are parallel, perpendicular, or neither, compare their slopes.

The slope of the first equation y = (4/3)x - 3 is 4/3.
The slope of the second equation y = (-3/4)x + 2 is -3/4.

Since the slopes are negative reciprocals of each other, the lines are perpendicular.

4.) To determine which set of points are collinear, you need to check if the slope between any two points is the same. Collinear points lie on the same line.

For set A(-1, 5); B(2, 6); C(4, 7):
Slope of AB = (6 - 5) / (2 - (-1)) = 1/3
Slope of BC = (7 - 6) / (4 - 2) = 1/2

Since the slopes are not equal, points A, B, and C are not collinear.

For set A(0, 0); B(1/2, 3); C(1, 5):
Slope of AB = (3 - 0) / (1/2 - 0) = 6
Slope of BC = (5 - 3) / (1 - 1/2) = 4

Since the slopes are not equal, points A, B, and C are not collinear.

For set A(-4, -2); B(0, -4); C(2, -5):
Slope of AB = (-4 - (-2)) / (0 - (-4)) = -2/4 = -1/2
Slope of BC = (-5 - (-4)) / (2 - 0) = -1/2

Since the slopes are equal, points A, B, and C are collinear.

Therefore, the set A(-4, -2); B(0, -4); C(2, -5) is collinear.

5.) To determine if the lines 4x - 6y = 9 and 3y - 2x = 7j are parallel, perpendicular, or neither, compare their slopes.

Rewrite the equations in slope-intercept form:
4x - 6y = 9 => y = (4/6)x - 9/6 => y = (2/3)x - 3/2 (slope = 2/3)
3y - 2x = 7j => y = (2/3)x + 7j/3 (slope = 2/3)

Since the slopes are equal, the lines are parallel.

6.) To determine if the lines 4x - 6y = 9 and 4y + 6x = 12 are parallel, perpendicular, or neither, compare their slopes.

Rewrite the equations in slope-intercept form:
4x - 6y = 9 => y = (4/6)x - 9/6 => y = (2/3)x - 3/2 (slope = 2/3)
4y + 6x = 12 => y = (-6/4)x + 12/4 => y = (-3/2)x + 3 (slope = -3/2)

Since the slopes are negative reciprocals of each other, the lines are perpendicular.

7.) To determine if the lines 4x - 6y = 9 and 3x - 2y = 11 are parallel, perpendicular, or neither, compare their slopes.

Rewrite the equations in slope-intercept form:
4x - 6y = 9 => y = (4/6)x - 9/6 => y = (2/3)x - 3/2 (slope = 2/3)
3x - 2y = 11 => y = (3/2)x - 11/2 (slope = 3/2)

Since the slopes are not equal and not negative reciprocals, the lines are neither parallel nor perpendicular.

8.) To determine if the lines formed by the sides of triangle ΔABC are parallel, perpendicular, or neither, compare their slopes.

Given the vertices A(2,5), B(8,1), and C(-2,-1).

The slope of AB = (1 - 5) / (8 - 2) = -4/6 = -2/3.
The slope of AC = (-1 - 5) / (-2 - 2) = -6/-4 = 3/2.

Since the slopes are negative reciprocals of each other, the lines AB and AC are perpendicular.

Therefore, the lines forming the sides of triangle ΔABC are perpendicular.