For 1-10, determine whether the lines are parallel, perpendicular or neither.

One line passes through the points (-1, 4) and (2, 6); another line passes through the points (2, -3) and (8, 1).
One line passes through the points (4, -3) and (-8, 0); another line passes through the points (-1, -1) and (-2, 6).
One line passes through the points (-3, 14) and (1, -2); another line passes through the points (0, -3) and (-2, 5).
One line passes through the points (3, 3) and (-6, -3); another line passes through the points (2, -8) and (-6, 4).
Both lines pass through the point (2, 8); one line also passes through (3, 5), and the other line has slope 3.

I see 4 questions of the same type, with just different numbers.

The last one uses the same concepts, just stated in a different way.

I will do the 1st:
slope between the points (-1, 4) and (2, 6) = (6-4)/(2-(-1)) = 2/3
slope between the points (2, -3) and (8, 1) = (1-(-3))/(8-2) = 4/6 = 2/3

Since the slopes are the same, the lines are parallel

(If the lines are perpendicular, their slopes would be opposite reciprocals
e.g. 6/7 vs -7/6 , or -4/3 vs 3/4 )

1. Neither. They just wave at each other from a distance.

2. Perpendicular. They're like two lines intersecting at a right angle, ready to square dance.
3. Neither. They're like two cars trying to parallel park but not even close.
4. Perpendicular. They're like two lines meeting up for a high-five in the sky.
5. Neither. They're like two lines trying to hug, but they just miss each other.
6. Neither. They're like two lines trying to have a conversation, but they just talk past each other.
7. Perpendicular. They're like two lines getting tangled up in a crazy dance move.
8. Neither. They're like two lines that are just lost and can't find each other.
9. Perpendicular. They're like two lines that are finally aligned and ready to take on the world.
10. Neither. They're like two lines on a roller coaster ride, going in different directions.

To determine whether the lines are parallel, perpendicular, or neither, we need to compare their slopes.

1. Line 1 passes through the points (-1, 4) and (2, 6), and Line 2 passes through the points (2, -3) and (8, 1).
The slope of Line 1 is (6 - 4) / (2 - (-1)) = 2 / 3.
The slope of Line 2 is (1 - (-3)) / (8 - 2) = 4 / 6 = 2 / 3.
Since both slopes are the same, the lines are parallel.

2. Line 1 passes through the points (4, -3) and (-8, 0), and Line 2 passes through the points (-1, -1) and (-2, 6).
The slope of Line 1 is (0 - (-3)) / (-8 - 4) = 3 / (-12) = -1 / 4.
The slope of Line 2 is (6 - (-1)) / (-2 - (-1)) = 7 / (-1) = -7.
Since the slopes are different, the lines are neither parallel nor perpendicular.

3. Line 1 passes through the points (-3, 14) and (1, -2), and Line 2 passes through the points (0, -3) and (-2, 5).
The slope of Line 1 is (-2 - 14) / (1 - (-3)) = -16 / 4 = -4.
The slope of Line 2 is (5 - (-3)) / (-2 - 0) = 8 / (-2) = -4.
Since the slopes are the same, the lines are parallel.

4. Line 1 passes through the points (3, 3) and (-6, -3), and Line 2 passes through the points (2, -8) and (-6, 4).
The slope of Line 1 is (-3 - 3) / (-6 - 3) = -6 / (-9) = 2 / 3.
The slope of Line 2 is (4 - (-8)) / (-6 - 2) = 12 / (-8) = -3 / 2.
Since the slopes are different, the lines are neither parallel nor perpendicular.

5. Both lines pass through the point (2, 8), and Line 1 also passes through (3, 5), with slope = 3.
The slope of Line 2 is not given.
We can find the slope of Line 2 using the midpoint formula: (y2 - y1) / (x2 - x1).
For Line 2, the midpoint between (2, 8) and (3, 5) is ((2 + 3) / 2, (8 + 5) / 2) = (2.5, 6.5).
The slope of Line 2 using (2, 8) and (2.5, 6.5) is (6.5 - 8) / (2.5 - 2) = -1.5 / 0.5 = -3.
Since the slope of Line 2 is -3 and the slope of Line 1 is 3, the lines are perpendicular.

To determine whether two lines are parallel, perpendicular, or neither, we need to compare their slopes. The slope of a line can be found using the formula:

Slope = (y2 - y1) / (x2 - x1)

Let's calculate the slopes for each pair of points given in the problem and compare them.

1) Line through (-1, 4) and (2, 6):
Slope = (6 - 4) / (2 - (-1)) = 2 / 3

Line through (2, -3) and (8, 1):
Slope = (1 - (-3)) / (8 - 2) = 4 / 6 = 2 / 3

The slopes of both lines are equal (2/3), so they are parallel.

2) Line through (4, -3) and (-8, 0):
Slope = (0 - (-3)) / (-8 - 4) = 3 / (-12) = -1/4

Line through (-1, -1) and (-2, 6):
Slope = (6 - (-1)) / (-2 - (-1)) = 7 / (-1) = -7

The slopes of the two lines are different (-1/4 and -7), so they are neither parallel nor perpendicular.

3) Line through (-3, 14) and (1, -2):
Slope = (-2 - 14) / (1 - (-3)) = -16 / 4 = -4

Line through (0, -3) and (-2, 5):
Slope = (5 - (-3)) / (-2 - 0) = 8 / (-2) = -4

The slopes of both lines are equal (-4), so they are parallel.

4) Line through (3, 3) and (-6, -3):
Slope = (-3 - 3) / (-6 - 3) = -6 / (-9) = 2/3

Line through (2, -8) and (-6, 4):
Slope = (4 - (-8)) / (-6 - 2) = 12 / (-8) = -3 / 2

The slopes of the two lines are different (2/3 and -3/2), so they are neither parallel nor perpendicular.

5) Both lines pass through (2, 8). One line also passes through (3, 5), and the other line has a slope of 3.

The slope between (2, 8) and (3, 5) is (5 - 8) / (3 - 2) = -3 / 1 = -3.

Since the second line has a slope of 3, which is the negative reciprocal of -3, the two lines are perpendicular.

To summarize:
1) The first pair of lines is parallel.
2) The second pair of lines is neither parallel nor perpendicular.
3) The third pair of lines is parallel.
4) The fourth pair of lines is neither parallel nor perpendicular.
5) The fifth pair of lines is perpendicular.

i dont get it