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

I caught #5

first equation : 4x - 6y = 9
multiply 2nd by -2 ---> 4x - 6y = 14j
what do you think now?

perpendicular

no, aren't their slopes equal ??

4x - 6y = ?????
the slope is 2/3, the constant on the right side does not matter.

oh ok

Choose whether the lines given below are parallel, perpendicular or neither.

Determine whether the lines are perpendicular, parallel or neither.

-x+2y= -2
2x-4y= 3

1.) To determine if AB and CD are parallel, perpendicular, or neither, we need to find the slopes of the two lines. The formula for finding the slope between two points (x1, y1) and (x2, y2) is given by m = (y2 - y1) / (x2 - x1). Let's calculate the slopes:

Slope of AB = (3 - 5) / (2 - (-4)) = -2 / 6 = -1/3
Slope of CD = (0 - 4) / (5 - 0) = -4 / 5

Since the slopes are not equal (they are not parallel) and not negative reciprocals of each other (they are not perpendicular), the lines AB and CD are neither parallel nor perpendicular.

2.) To determine if the lines y = 1x + 7 and y = 3x - 2 are parallel, perpendicular, or neither, we need to compare the slopes of the two lines. The slopes can be determined by comparing the coefficients of x. In this case, the slopes are 1 and 3, respectively.

Since the slopes are not equal (they are not parallel) and not negative reciprocals of each other (they are not perpendicular), the lines y = 1x + 7 and y = 3x - 2 are neither parallel nor perpendicular.

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

Since the slopes are negative reciprocals of each other (4/3 * -3/4 = -1), the lines y = 4/3x - 3 and y = -3/4x + 2 are perpendicular.

4.) To determine which set of points is collinear, we need to check if the slopes between each pair of points are equal. Let's calculate the slopes for each set of points:

Slope of A(-1,5), B(2,6) = (6 - 5) / (2 - (-1)) = 1 / 3
Slope of A(0,0), B(1/2,3) = (3 - 0) / (1/2 - 0) = 3 / (1/2) = 6
Slope of A(-4,-2), B(0,-4) = (-4 - (-2)) / (0 - (-4)) = -2 / 4 = -1/2

The set of points A(-1,5), B(2,6), C(4,7) has the same slope for all the points. Therefore, they are collinear.

5.) To determine if the lines 4x - 6y = 9 and 3y - 2x = 7 are parallel, perpendicular, or neither, we can compare the slopes. Rewrite the equations in slope-intercept form (y = mx + b) to find the slopes.

4x - 6y = 9 -> -6y = -4x + 9 -> y = (4/6)x - (9/6) -> y = (2/3)x - (3/2)
3y - 2x = 7 -> 3y = 2x + 7 -> y = (2/3)x + (7/3)

The slopes of both lines are 2/3. Since the slopes are equal (they are the same), the lines 4x - 6y = 9 and 3y - 2x = 7 are parallel.

6.) To determine if the lines 4x - 6y = 9 and 4y + 6x = 12 are parallel, perpendicular, or neither, we can compare the slopes after converting the equations to slope-intercept form.

4x - 6y = 9 -> -6y = -4x + 9 -> y = (4/6)x - (9/6) -> y = (2/3)x - (3/2)
4y + 6x = 12 -> 4y = -6x + 12 -> y = (-6/4)x + (12/4) -> y = (-3/2)x + 3

The slope of the first equation is 2/3, while the slope of the second equation is -3/2. Since the slopes are negative reciprocals of each other (2/3 * -3/2 = -1), the lines 4x - 6y = 9 and 4y + 6x = 12 are perpendicular.

7.) To determine if the lines 4x - 6y = 9 and 3x - 2y = 11 are parallel, perpendicular, or neither, we can compare the slopes after converting the equations to slope-intercept form.

4x - 6y = 9 -> -6y = -4x + 9 -> y = (4/6)x - (9/6) -> y = (2/3)x - (3/2)
3x - 2y = 11 -> -2y = -3x + 11 -> y = (3/2)x - (11/2)

The slopes of the lines are 2/3 and 3/2, respectively. Since the slopes are not equal (they are not parallel) and not negative reciprocals of each other (they are not perpendicular), the lines 4x - 6y = 9 and 3x - 2y = 11 are neither parallel nor perpendicular.

8.) To determine if the lines AB and AC are parallel, perpendicular, or neither, we need to compare their slopes. The slope of AB is given as -2/3 and the slope of AC is given as 3/2.

Since the slopes are negative reciprocals of each other, i.e., (-2/3) * (3/2) = -1, the lines AB and AC are perpendicular.