# Parallel and Perpendicular Lines Practice.

1. Y = -X
2. Y = -3/2x + 2
3. X = 4
4. Y = -2x - 1
5. Y = -1/2x + 5/2
6. Perpendicular
7. Parallel
8. Neither
9. Sometimes
10. Never

## To determine whether the given lines are parallel or perpendicular, we need to compare their slopes.

1. Line 1: y = -x
The slope of Line 1 is -1.

2. Line 2: y = (-3/2)x + 2
The slope of Line 2 is -3/2.

Comparing the slopes:
-1 is not equal to -3/2. Therefore, Line 1 and Line 2 are neither parallel nor perpendicular.

3. Line 3: x = 4
This is a vertical line with an undefined slope. (Parallel to the y-axis)

4. Line 4: y = -2x - 1
The slope of Line 4 is -2.

Comparing the slopes:
-2 is not equal to -3/2. Therefore, Line 4 is neither parallel nor perpendicular to Line 2.

5. Line 5: y = (-1/2)x + 5/2
The slope of Line 5 is -1/2.

Comparing the slopes:
-1/2 is not equal to -3/2. Therefore, Line 5 is neither parallel nor perpendicular to Line 2.

Based on the analysis above, the correct answers are:

6. Line 1 and Line 2 are neither parallel nor perpendicular.
7. Line 2 and Line 3 are parallel.
8. Line 4 and Line 2 are neither parallel nor perpendicular.
9. Line 5 and Line 2 are sometimes parallel.
10. Line 1 and Line 4 are never parallel.

## To determine whether two lines are parallel or perpendicular, we need to compare their slopes.

The slope-intercept form of a linear equation is y = mx + b, where "m" is the slope of the line.

For the first line, y = -x, the slope is -1.

For the second line, y = -3/2x + 2, the slope is -3/2.

For the third line, x = 4, this is a vertical line, and vertical lines have an undefined slope.

For the fourth line, y = -2x - 1, the slope is -2.

For the fifth line, y = -1/2x + 5/2, the slope is -1/2.

Now let's determine whether the pairs of lines are parallel, perpendicular, or neither based on their slopes:

6. The pair of lines is perpendicular if and only if the product of their slopes is -1. Since the first line has a slope of -1 and the second line has a slope of -3/2, their product is not -1. Therefore, the pair of lines is not perpendicular.

7. The pair of lines is parallel if and only if their slopes are equal. Since the first line has a slope of -1 and the second line has a slope of -3/2, their slopes are different. Therefore, the pair of lines is not parallel.

8. Neither parallel nor perpendicular - This means that the pair of lines does not meet the criteria for either parallel or perpendicular lines. Without specific line equations to compare, it is not possible to determine whether lines are parallel or perpendicular.

9. Sometimes - It is not specified which lines are being compared here, so it could refer to a situation where some lines are parallel and some are not.

10. Never - This means that two lines can never be parallel or perpendicular. In this case, it is not clear what lines are being referred to, so it is not possible to determine whether the statement is true or false.

Based on the given information, we can determine that the answer to question number 6 is "Neither," the answer to question number 7 is "Neither," and the answers to questions number 8, 9, and 10 cannot be determined without more specific information.